Shubin, M. A. (Mikhail Aleksandrovich) 1944
Overview
Works:  98 works in 304 publications in 3 languages and 3,475 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Honoree, Creator, Dedicatee 
Classifications:  QA377, 515.353 
Publication Timeline
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Most widely held works by
M. A Shubin
Pseudodifferential operators and spectral theory by
M. A Shubin(
Book
)
18 editions published between 1987 and 2001 in English and held by 469 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
18 editions published between 1987 and 2001 in English and held by 469 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
Foundations of the classical theory of partial differential equations by
I︠U︡. V Egorov(
Book
)
32 editions published between 1991 and 1998 in English and held by 298 WorldCat member libraries worldwide
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte fr Mathematik, 1993 "... It is comparable in scope with the great CourantHilbert "Methods of Mathematical Physics", but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. The book gives a good and readable overview of the subject. ... carefully written, well translated, and well produced." The Mathematical Gazette, 1993
32 editions published between 1991 and 1998 in English and held by 298 WorldCat member libraries worldwide
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte fr Mathematik, 1993 "... It is comparable in scope with the great CourantHilbert "Methods of Mathematical Physics", but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. The book gives a good and readable overview of the subject. ... carefully written, well translated, and well produced." The Mathematical Gazette, 1993
Partial differential equations VII : spectral theory of differential operators by
M. A Shubin(
Book
)
15 editions published between 1994 and 2011 in English and held by 263 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
15 editions published between 1994 and 2011 in English and held by 263 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
Partial differential equations III by
I︠U︡. V Egorov(
Book
)
14 editions published in 1991 in English and held by 232 WorldCat member libraries worldwide
14 editions published in 1991 in English and held by 232 WorldCat member libraries worldwide
The Schrödinger equation by
F. A Berezin(
Book
)
18 editions published between 1983 and 1991 in 3 languages and held by 209 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
18 editions published between 1983 and 1991 in 3 languages and held by 209 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
Partial differential equations by
M. V Fedori︠u︡k(
Book
)
11 editions published between 1993 and 1997 in 3 languages and held by 199 WorldCat member libraries worldwide
11 editions published between 1993 and 1997 in 3 languages and held by 199 WorldCat member libraries worldwide
Partial differential equations VI : elliptic and parabolic operators by
I︠U︡. V Egorov(
Book
)
14 editions published in 1994 in English and held by 193 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
14 editions published in 1994 in English and held by 193 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
Partial differential equations IV : microlocal analysis and hyperbolic equations by
I︠U︡. V Egorov(
Book
)
15 editions published between 1992 and 2011 in English and Undetermined and held by 192 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
15 editions published between 1992 and 2011 in English and Undetermined and held by 192 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 II : elements of the modern theory ; equations with constant coefficients(
Book
)
13 editions published in 1994 in English and held by 187 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
13 editions published in 1994 in English and held by 187 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 IX : elliptic boundary value problems by
M. S Agranovich(
Book
)
10 editions published in 1997 in English and held by 161 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
10 editions published in 1997 in English and held by 161 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 : Mark Vishik's seminar by
M. I Vishik(
Book
)
5 editions published in 2002 in English and held by 160 WorldCat member libraries worldwide
5 editions published in 2002 in English and held by 160 WorldCat member libraries worldwide
Partial differential equations by
M. A Shubin(
Book
)
10 editions published in 1996 in English and held by 150 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
10 editions published in 1996 in English and held by 150 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
Elements of the modern theory of partial differential equations by
I︠U︡. V Egorov(
Book
)
9 editions published between 1994 and 1999 in English and held by 103 WorldCat member libraries worldwide
9 editions published between 1994 and 1999 in English and held by 103 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
)
7 editions published between 2010 and 2011 in English and held by 94 WorldCat member libraries worldwide
7 editions published between 2010 and 2011 in English and held by 94 WorldCat member libraries worldwide
Spectral theory and geometric analysis : international conference in honor of Mikhail Shubin's 65th birthday, spectral theory
and geometric analysis, July 29  August 2, 2009, Northeastern University, Boston, MA(
Book
)
7 editions published in 2011 in English and held by 60 WorldCat member libraries worldwide
7 editions published in 2011 in English and held by 60 WorldCat member libraries worldwide
Elements of the modern theory ; Equations with constant coefficients(
Book
)
2 editions published in 1994 in English and held by 42 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 42 WorldCat member libraries worldwide
Partial differential equations VII : spectral theory of differential equations(
Book
)
1 edition published in 1994 in English and held by 18 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 18 WorldCat member libraries worldwide
Topics in statistical and theoretical physics : F.A. Berezin memorial volume(
Book
)
3 editions published in 1996 in English and held by 16 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 16 WorldCat member libraries worldwide
Psevdodifferent︠s︡ialʹnye operatory i spektralʹnai︠a︡ teorii︠a︡ by
M. A Shubin(
Book
)
3 editions published in 1978 in Russian and held by 14 WorldCat member libraries worldwide
3 editions published in 1978 in Russian and held by 14 WorldCat member libraries worldwide
The Cauchy problem ; Qualitative theory of partial differential equations(
Book
)
2 editions published in 1991 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 14 WorldCat member libraries worldwide
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Related Identities
 Egorov, I︠U︡. V. (I︠U︡riĭ Vladimirovich) Other Author Editor Creator
 Agranovich, M. S. Author Editor
 Berezin, F. A. (Feliks Aleksandrovich) Honoree Author
 Braverman, Maxim 1966 Editor
 Vishik, M. I. Author
 Rozenblum, G. V. Author
 Solomi︠a︡k, M. Z.
 Komech, A. I. Creator
 Agranovič, Michail S.
 Andersson, Stig Ingvar Translator
Useful Links
Associated Subjects
Berezin, F. A.(Feliks Aleksandrovich) Boundary value problems ChemistryMathematics Differential equations Differential equations, Elliptic Differential equations, Hyperbolic Differential equations, Linear Differential equations, Partial Differential operators Elliptic operators Engineering Functional analysis Geometric analysis Global analysis (Mathematics) Global differential geometry Hamiltonian systems Mathematical physics Mathematics Microlocal analysis Parabolic operators Pseudodifferential operators Quantum theory Schrödinger equation Spectral theory (Mathematics) Statistical physics
Alternative Names
Mikhail Shubin AmericanRussian mathematician
Schubin, M. A. 1944
Shubin, M.
Shubin, M. 1944
Shubin, M. A.
Shubin, M.A. 1944
Shubin, Michail A. 1944
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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