Duistermaat, J. J. (Johannes Jisse) 1942
Overview
Works:  40 works in 228 publications in 5 languages and 5,268 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Honoree, Dedicatee 
Classifications:  QA614.833, 516.36 
Publication Timeline
.
Most widely held works by
J. J Duistermaat
Geometry of nonholonomically constrained systems
by
Richard H Cushman(
)
16 editions published between 2009 and 2010 in English and held by 1,138 WorldCat member libraries worldwide
This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Carathéodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat. The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trailblazers in their respective fields
16 editions published between 2009 and 2010 in English and held by 1,138 WorldCat member libraries worldwide
This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Carathéodory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all motions of the disk, including those where the disk falls flat and those where it nearly falls flat. The geometric techniques described in this book for symmetry reduction have not appeared in any book before. Nor has the detailed description of the motion of the rolling disk. In this respect, the authors are trailblazers in their respective fields
Fourier integral operators
by
J. J Duistermaat(
Book
)
38 editions published between 1972 and 2011 in English and Undetermined and held by 946 WorldCat member libraries worldwide
This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hörmander's exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. WKBmethods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a onesemester introductory course on Fourier integral operators aimed at a broad audience. This book remains a superb introduction to the theory of Fourier integral operators. While there are further advances discussed in other sources, this book can still be recommended as perhaps the very best place to start in the study of this subject. SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. Zentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. Acta Sci. Math
38 editions published between 1972 and 2011 in English and Undetermined and held by 946 WorldCat member libraries worldwide
This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hörmander's exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. WKBmethods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a onesemester introductory course on Fourier integral operators aimed at a broad audience. This book remains a superb introduction to the theory of Fourier integral operators. While there are further advances discussed in other sources, this book can still be recommended as perhaps the very best place to start in the study of this subject. SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. Zentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. Acta Sci. Math
Differentiation
by
J. J Duistermaat(
)
43 editions published between 2003 and 2009 in English and held by 654 WorldCat member libraries worldwide
Part one of the authors' comprehensive and innovative work on multidimensional real analysis. Numerous illustrative exercises combined with an exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study
43 editions published between 2003 and 2009 in English and held by 654 WorldCat member libraries worldwide
Part one of the authors' comprehensive and innovative work on multidimensional real analysis. Numerous illustrative exercises combined with an exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study
The heat kernel Lefschetz fixed point formula for the spinc dirac operator
by
J. J Duistermaat(
)
27 editions published between 1995 and 2011 in English and Italian and held by 579 WorldCat member libraries worldwide
Interest in the spinc Dirac operator originally came about from the study of complex analytic manifolds, where in the nonKähler casethe Dolbeault operator is no longer suitable for getting local formulas for the RiemannRoch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spinc Dirac operator. Using the heat kernels theory of Berline, Getzler, and Vergne,this workrevisits some fundamental concepts of the theory, and presents the application to symplectic geometry. J.J. Duistermaat was well known for his beautiful and concise expositions of seemingly familiar concepts, and this classic studyis certainly no exception. Reprinted as it was originally published,this workis as an affordable textthat will be of interest to a range of researchers in geometric analysis and mathematical physics. Overall this is a carefully written, highly readable book on a very beautiful subject. Mathematical Reviews The book of J.J. Duistermaat is a nice introduction to analysis related[to the]spinc Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. EMS Newsletter The author's book is a marvelous introduction to [these] objects and theories. Zentralblatt MATH
27 editions published between 1995 and 2011 in English and Italian and held by 579 WorldCat member libraries worldwide
Interest in the spinc Dirac operator originally came about from the study of complex analytic manifolds, where in the nonKähler casethe Dolbeault operator is no longer suitable for getting local formulas for the RiemannRoch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spinc Dirac operator. Using the heat kernels theory of Berline, Getzler, and Vergne,this workrevisits some fundamental concepts of the theory, and presents the application to symplectic geometry. J.J. Duistermaat was well known for his beautiful and concise expositions of seemingly familiar concepts, and this classic studyis certainly no exception. Reprinted as it was originally published,this workis as an affordable textthat will be of interest to a range of researchers in geometric analysis and mathematical physics. Overall this is a carefully written, highly readable book on a very beautiful subject. Mathematical Reviews The book of J.J. Duistermaat is a nice introduction to analysis related[to the]spinc Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. EMS Newsletter The author's book is a marvelous introduction to [these] objects and theories. Zentralblatt MATH
Discrete integrable systems QRT Maps and Elliptic Surfaces
by
J. J Duistermaat(
)
15 editions published between 2010 and 2014 in English and held by 455 WorldCat member libraries worldwide
This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The application of QRT maps to problems in the literature, including Poncelet mapping and the elliptic billiard, is examined
15 editions published between 2010 and 2014 in English and held by 455 WorldCat member libraries worldwide
This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The application of QRT maps to problems in the literature, including Poncelet mapping and the elliptic billiard, is examined
Distributions theory and applications
by
J. J Duistermaat(
)
15 editions published between 2008 and 2010 in English and held by 407 WorldCat member libraries worldwide
"This textbook is an applicationoriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background."Publisher's description
15 editions published between 2008 and 2010 in English and held by 407 WorldCat member libraries worldwide
"This textbook is an applicationoriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background."Publisher's description
Lie groups
by
J. J Duistermaat(
Book
)
15 editions published between 1999 and 2000 in English and Portuguese and held by 376 WorldCat member libraries worldwide
"This is a (post)graduate textbook an Lie groups and Lie algebras. Its aim is to give a broad introduction to the field with an emphasis on using differentialgeometrical methods, in the spirit of Lie himself. The structure of compact Lie groups is analyzed in terms of the action of the group on itself by conjugation. The book culminates in the classification of the representations of compact Lie groups and in their realization as sections of holomorphic line bundles over flag manifolds. The relations with algebraic and analytic models are also discussed. A review of the required background material is provided in appendices."Jacket
15 editions published between 1999 and 2000 in English and Portuguese and held by 376 WorldCat member libraries worldwide
"This is a (post)graduate textbook an Lie groups and Lie algebras. Its aim is to give a broad introduction to the field with an emphasis on using differentialgeometrical methods, in the spirit of Lie himself. The structure of compact Lie groups is analyzed in terms of the action of the group on itself by conjugation. The book culminates in the classification of the representations of compact Lie groups and in their realization as sections of holomorphic line bundles over flag manifolds. The relations with algebraic and analytic models are also discussed. A review of the required background material is provided in appendices."Jacket
Integration
by
J. J Duistermaat(
)
4 editions published in 2004 in English and held by 258 WorldCat member libraries worldwide
4 editions published in 2004 in English and held by 258 WorldCat member libraries worldwide
Mathematics past and present : Fourier integral operators : selected classical articles
by
J. J Duistermaat(
Book
)
8 editions published in 1994 in English and held by 215 WorldCat member libraries worldwide
8 editions published in 1994 in English and held by 215 WorldCat member libraries worldwide
Geometric aspects of analysis and mechanics in honor of the 65th birthday of Hans Duistermaat
by
Erik P. van den Ban(
Book
)
6 editions published in 2011 in English and held by 85 WorldCat member libraries worldwide
6 editions published in 2011 in English and held by 85 WorldCat member libraries worldwide
Classical aspects of partial differential equations
by
J. J Duistermaat(
Book
)
3 editions published in 1980 in English and held by 47 WorldCat member libraries worldwide
3 editions published in 1980 in English and held by 47 WorldCat member libraries worldwide
Energy and entropy as real morphisms for addition and order
by
J. J Duistermaat(
Book
)
6 editions published in 1968 in English and Undetermined and held by 21 WorldCat member libraries worldwide
6 editions published in 1968 in English and Undetermined and held by 21 WorldCat member libraries worldwide
Analyse van gewone differentiaalvergelijkingen
by
J. J Duistermaat(
Book
)
2 editions published between 1995 and 2002 in Dutch and held by 19 WorldCat member libraries worldwide
Studieboek voor het universitair onderwijs
2 editions published between 1995 and 2002 in Dutch and held by 19 WorldCat member libraries worldwide
Studieboek voor het universitair onderwijs
Journées complexes de Metz, février 1972 : [équations différentielles et fonctions de plusieurs variables
(
Book
)
2 editions published in 1973 in French and held by 17 WorldCat member libraries worldwide
2 editions published in 1973 in French and held by 17 WorldCat member libraries worldwide
Fourier integral operators
by
J. J Duistermaat(
)
2 editions published in 2011 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 2011 in English and held by 8 WorldCat member libraries worldwide
Geometric aspects of analysis and mechanics in honor of the 65th birthday of Hans Duistermaat
(
)
1 edition published in 2011 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 6 WorldCat member libraries worldwide
Equations différentielles et fonctions de plusieurs variables : Metz, France, 2225 février 1972
by Journées Complexes(
Book
)
1 edition published in 1973 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 1973 in French and held by 5 WorldCat member libraries worldwide
QRT maps and elliptic surfaces
by
J. J Duistermaat(
Book
)
1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 4 WorldCat member libraries worldwide
Multidimensional real analysis
(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
Multidimensional real analysis
(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Kolk, Johan A. C. 1947 Editor
 Cushman, Richard H. 1942 Author
 Śniatycki, Jędrzej
 Braam Houckgeest, J. P. van Translator
 Hormander, Lars
 Brüning, Jochen Editor
 Guillemin, Victor 1937 Editor
 Ban, Erik P. van den Editor
 Eckhaus, W. (Wiktor) 19302000
 Kolk, Johan A.
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Associated Subjects
Almost complex manifolds Caratheodory measure Differential equations Differential equations, Partial Differential topology Dirac equation Distribution (Probability theory) Elliptic surfaces Entropy Force and energy Forms (Mathematics) Fourier analysis Fourier integral operators Fourier series Fourier transformations Functional analysis Functions of complex variables Functions of real variables Functions of several complex variables Geometric analysis Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Global differential geometry Group theory Integral equations Lie groups Mappings (Mathematics) Mathematical analysis Mathematical physics Mathematics Nonholonomic dynamical systems Number theory Operator theory Physics Rigidity (Geometry) Science Sobolev spaces Theory of distributions (Functional analysis) Topological groups
Alternative Names
Duistermaat, H. 19422010
Duistermaat, Hans.
Duistermaat, Hans 19422010
Duistermaat, J. 19422010
Duistermaat, J. J.
Duistermaat, J. J. 19422010
Duistermaat, Johannes 19422010
Duistermaat, Johannes J.
Duistermaat, Johannes Jisse
Duistermaat, Johannes Jisse 1942
Duistermaat, Johannes Jisse 19422010
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