Shubin, M. A. (Mikhail Aleksandrovich) 1944
Overview
Works:  69 works in 385 publications in 3 languages and 4,403 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Creator, Dedicatee, ed 
Publication Timeline
.
Most widely held works by
M. A Shubin
Partial differential equations VII : spectral theory of differential operators by
I︠U︡. V Egorov(
Book
)
73 editions published between 1991 and 2010 in English and held by 663 WorldCat member libraries worldwide
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finitedimensional spaces. The basic notions and theorems are first reviewed and followed by a comprehensive presentation of a variety of advanced approaches such as the factorization method, the variational techniques, the approximate spectral projection method, and the probabilistic method, to name a few. Special attention is devoted to the spectral properties of Schrödinger and Dirac operators and of other operators as well. In addition, a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum" is included
73 editions published between 1991 and 2010 in English and held by 663 WorldCat member libraries worldwide
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finitedimensional spaces. The basic notions and theorems are first reviewed and followed by a comprehensive presentation of a variety of advanced approaches such as the factorization method, the variational techniques, the approximate spectral projection method, and the probabilistic method, to name a few. Special attention is devoted to the spectral properties of Schrödinger and Dirac operators and of other operators as well. In addition, a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum" is included
Pseudodifferential operators and spectral theory by
M. A Shubin(
Book
)
26 editions published between 1986 and 2012 in English and held by 499 WorldCat member libraries worldwide
This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers
26 editions published between 1986 and 2012 in English and held by 499 WorldCat member libraries worldwide
This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers
Partial differential equations : Mark Vishik's seminar by
M. S Agranovich(
Book
)
24 editions published between 1997 and 2002 in 3 languages and held by 366 WorldCat member libraries worldwide
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameterdependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities
24 editions published between 1997 and 2002 in 3 languages and held by 366 WorldCat member libraries worldwide
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameterdependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities
Partial differential equations II : elements of the modern theory ; equations with constant coefficients(
Book
)
19 editions published between 1991 and 1994 in English and held by 254 WorldCat member libraries worldwide
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics
19 editions published between 1991 and 1994 in English and held by 254 WorldCat member libraries worldwide
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics
Partial differential equations III by
I︠U︡. V Egorov(
Book
)
19 editions published in 1991 in English and held by 244 WorldCat member libraries worldwide
19 editions published in 1991 in English and held by 244 WorldCat member libraries worldwide
Partial differential equations IV : microlocal analysis and hyperbolic equations by
I︠U︡. V Egorov(
Book
)
28 editions published between 1991 and 2011 in English and Undetermined and held by 220 WorldCat member libraries worldwide
In the first part of this EMS volume Yu. V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V. Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C? and L2 wellposedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics
28 editions published between 1991 and 2011 in English and Undetermined and held by 220 WorldCat member libraries worldwide
In the first part of this EMS volume Yu. V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V. Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C? and L2 wellposedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics
Partial differential equations VI : elliptic and parabolic operators by
I︠U︡. V Egorov(
Book
)
22 editions published between 1991 and 1994 in English and held by 216 WorldCat member libraries worldwide
This volume of the EMS contains three contributions covering topics in the field of partial differential equations: Elliptic operators on closed manifolds, degenerating elliptic equations and boundary problems, and parabolic equations. All the authors are wellknown researchers and they present their material as accessible surveys enabling readers to find comprehensive coverage of results which are scattered throughout the literature. For this reason the book is a unique source of information. It forms part of a multivolume subseries of the EMS devoted to partial differential equations and it will be very useful to graduate students and researchers in mathematics and theoretical physics as well as engineers who are interested in this subject
22 editions published between 1991 and 1994 in English and held by 216 WorldCat member libraries worldwide
This volume of the EMS contains three contributions covering topics in the field of partial differential equations: Elliptic operators on closed manifolds, degenerating elliptic equations and boundary problems, and parabolic equations. All the authors are wellknown researchers and they present their material as accessible surveys enabling readers to find comprehensive coverage of results which are scattered throughout the literature. For this reason the book is a unique source of information. It forms part of a multivolume subseries of the EMS devoted to partial differential equations and it will be very useful to graduate students and researchers in mathematics and theoretical physics as well as engineers who are interested in this subject
The Schrödinger equation by
F. A Berezin(
Book
)
16 editions published in 1991 in English and held by 206 WorldCat member libraries worldwide
This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the onedimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multidimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the onedimensional case. Chapter 4 presents the scattering theory for the multidimensional nonrelativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication
16 editions published in 1991 in English and held by 206 WorldCat member libraries worldwide
This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the onedimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multidimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the onedimensional case. Chapter 4 presents the scattering theory for the multidimensional nonrelativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication
Contemporary mathematical physics : F.A. Berezin memorial volume by
R. L Dobrushin(
Book
)
4 editions published in 1996 in English and held by 187 WorldCat member libraries worldwide
This first of a twovolume collection is a celebration of the scientific heritage of F. A. Berezin (19311980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics
4 editions published in 1996 in English and held by 187 WorldCat member libraries worldwide
This first of a twovolume collection is a celebration of the scientific heritage of F. A. Berezin (19311980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics
Topics in statistical and theoretical physics : F.A. Berezin memorial volume by
R. L Dobrushin(
Book
)
5 editions published in 1996 in English and held by 185 WorldCat member libraries worldwide
This is the second of two volumes dedicated to the scientific heritage of F. A. Berezin (19311980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization and Grassmannian analysis ("supermathematics"). Collected here are papers by many of his colleagues and others who worked in related areas, representing a wide spectrum of topics in statistical a
5 editions published in 1996 in English and held by 185 WorldCat member libraries worldwide
This is the second of two volumes dedicated to the scientific heritage of F. A. Berezin (19311980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization and Grassmannian analysis ("supermathematics"). Collected here are papers by many of his colleagues and others who worked in related areas, representing a wide spectrum of topics in statistical a
Partial differential equations by
M. A Shubin(
Book
)
20 editions published between 1991 and 1996 in English and held by 178 WorldCat member libraries worldwide
This volume contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schrodinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the AtiyahSinger index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples
20 editions published between 1991 and 1996 in English and held by 178 WorldCat member libraries worldwide
This volume contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schrodinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the AtiyahSinger index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples
Partial differential equations(
Book
)
in English and Undetermined and held by 172 WorldCat member libraries worldwide
in English and Undetermined and held by 172 WorldCat member libraries worldwide
Spectral theory and geometric analysis : international conference in honor of Mikhail Shubin's 65th birthday, July 29  August
2, 2009, Northeastern University, Boston, Massachusetts(
Book
)
14 editions published between 2010 and 2011 in English and held by 163 WorldCat member libraries worldwide
14 editions published between 2010 and 2011 in English and held by 163 WorldCat member libraries worldwide
Elements of the modern theory of partial differential equations by
I︠U︡. V Egorov(
Book
)
14 editions published between 1992 and 1999 in English and German and held by 120 WorldCat member libraries worldwide
14 editions published between 1992 and 1999 in English and German and held by 120 WorldCat member libraries worldwide
Uravnenie Shredingera by
F. A Berezin(
Book
)
7 editions published in 1983 in Russian and Undetermined and held by 22 WorldCat member libraries worldwide
7 editions published in 1983 in Russian and Undetermined and held by 22 WorldCat member libraries worldwide
The Cauchy problem ; Qualitative theory of partial differential equations(
Book
)
3 editions published in 1991 in English and held by 17 WorldCat member libraries worldwide
3 editions published in 1991 in English and held by 17 WorldCat member libraries worldwide
Psevdodifferent︠s︡ialʹnye operatory i spektralʹnai︠a︡ teorii︠a︡ by
M. A Shubin(
Book
)
4 editions published between 1978 and 2005 in Russian and held by 17 WorldCat member libraries worldwide
4 editions published between 1978 and 2005 in Russian and held by 17 WorldCat member libraries worldwide
Psevdodifferencial' nye operatory i spektral'naja teorija by
M. A Shubin(
Book
)
9 editions published between 1978 and 2005 in Russian and Undetermined and held by 16 WorldCat member libraries worldwide
9 editions published between 1978 and 2005 in Russian and Undetermined and held by 16 WorldCat member libraries worldwide
Complexes of differential operators by
N. N Tarkhanov(
Book
)
1 edition published in 1990 in Russian and held by 13 WorldCat member libraries worldwide
The main topic is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one (that is, complexes of partial differential operators on an open subset of R [superscript n]), are often similar in content, the invariant language permits the simplification of the notation and reveals the algebraic nature of some questions more clearly. The last few decades have seen the delineation of the following directions within the general theory of complexes of differential operators: the formal theory; the existence theory; the problem of global solvability; overdetermined boundary problems; the generalised Lefschetz theory of fixed points; and the qualitative theory of solutions of overdetermined systems. All of these fields are treated here to some degree. Considerable attention is given to connections and parallels with the theory of functions of several complex variables
1 edition published in 1990 in Russian and held by 13 WorldCat member libraries worldwide
The main topic is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one (that is, complexes of partial differential operators on an open subset of R [superscript n]), are often similar in content, the invariant language permits the simplification of the notation and reveals the algebraic nature of some questions more clearly. The last few decades have seen the delineation of the following directions within the general theory of complexes of differential operators: the formal theory; the existence theory; the problem of global solvability; overdetermined boundary problems; the generalised Lefschetz theory of fixed points; and the qualitative theory of solutions of overdetermined systems. All of these fields are treated here to some degree. Considerable attention is given to connections and parallels with the theory of functions of several complex variables
The analysis of solutions of elliptic equations by
N. N Tarkhanov(
Book
)
2 editions published in 1991 in Russian and held by 8 WorldCat member libraries worldwide
This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on illposedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts
2 editions published in 1991 in Russian and held by 8 WorldCat member libraries worldwide
This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on illposedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts
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Related Identities
 Egorov, I︠U︡. V. (I︠U︡riĭ Vladimirovich) Other Author Editor Creator
 Berezin, F. A. (Feliks Aleksandrovich) Honoree Author
 Agranovich, M. S. Author Editor
 Dobrushin, R. L. 19291995 Author Editor
 Minlos, R. A. (Robert Adolʹfovich) Editor
 Vershik, A. M. (Anatoliĭ Moiseevich) 1933 Editor
 Sosinskiĭ, A. B. (Alekseĭ Bronislavovich) Translator
 Braverman, Maxim 1966 Editor
 Vishik, M. I. Author
 Rozenblum, G. V. Author
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Associated Subjects
Berezin, F. A.(Feliks Aleksandrovich) Boundary value problems ChemistryMathematics Complexes Differential equations, Elliptic Differential equations, EllipticNumerical solutions Differential equations, Hyperbolic Differential equations, Linear Differential equations, Partial Differential operators Elliptic operators Engineering Functional analysis Geometric analysis Geometry, Algebraic Global analysis (Mathematics) Global differential geometry Hamiltonian systems Laurent series Mathematical analysis Mathematical physics Mathematics Microlocal analysis Number theory Parabolic operators Potential theory (Mathematics) Pseudodifferential operators Quantum theory Representations of groups Schrödinger equation Spectral theory (Mathematics) Statistical physics
Alternative Names
Mikhail Shubin AmericanRussian mathematician
Mikhail Shubin Amerikaans wiskundige
Schubin, M. A. 1944
Shubin, M.
Shubin, M. 1944
Shubin, M.A.
Shubin, M.A. 1944
Shubin, Michail A. 1944
Shubin, Mikhail
Shubin, Mikhail 1944
Shubin, Mikhail A. 1944
Shubin, Mikhail Aleksandrovich
Shubin, Mikhail Aleksandrovich 1944...
Šubin, M. A.
Šubin, M. A. 1944
Šubin, Michail Aleksandrovič
Šubin, Michail Aleksandrovič 1944
Šubin, Michail Aleksandrovič. [t]
Šubin, Mikhail A. 1944
Шубин, Михаил Александрович.
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