J.J. Duistermaat's Books

Lie Groups

By: J.J. Duistermaat,Johan A.C. Kolk

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This (post) graduate text gives a broad introduction to Lie groups and algebras with an emphasis on differential geometrical methods. It analyzes the structure of compact Lie groups in terms of the action of the group on itself by conjugation, culminating in the classification of the representations of compact Lie groups and their realization as sections of holomorphic line bundles over flag manifolds. Appendices provide background reviews.

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Page Count

352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642569366

ISBN 13

9783642569364

Fourier Integral Operators

By: J.J. Duistermaat

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Fourier Integral Operators

By: J.J. Duistermaat

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 application 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, rep. WKB-methods.

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Page Count

160

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817638210

ISBN 13

9780817638214

Multidimensional Real Analysis I

Differentiation

By: J. J. Duistermaat,J. A. C. Kolk

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Multidimensional Real Analysis I

Differentiation

By: J. J. Duistermaat,J. A. C. Kolk

Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the 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.

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Page Count

444

Publisher

Cambridge University Press

Published Date

ISBN 10

1139451197

ISBN 13

9781139451192

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

By: J.J. Duistermaat

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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

By: J.J. Duistermaat

When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester , I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995.

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245

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Springer Science & Business Media

Published Date

ISBN 10

1461253446

ISBN 13

9781461253440

Mathematics Past and Present Fourier Integral Operators

By: J.J. Duistermaat,Victor W Guillemin,Jochen Brüning,L. Hörmander

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Mathematics Past and Present Fourier Integral Operators

By: J.J. Duistermaat,Victor W Guillemin,Jochen Brüning,L. Hörmander

What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hörmander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well.

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Page Count

300

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540567410

ISBN 13

9783540567417

Discrete Integrable Systems

QRT Maps and Elliptic Surfaces

By: J.J. Duistermaat

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Discrete Integrable Systems

QRT Maps and Elliptic Surfaces

By: J.J. Duistermaat

This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The theory of QRT maps arose from problems in mathematical physics, involving difference equations. The application of QRT maps to these and other problems in the literature, including Poncelet mapping and the elliptic billiard, is examined in detail. The link between elliptic fibrations and completely integrable Hamiltonian systems is also discussed. The book begins with a comprehensive overview of the subject, including QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, action on homology classes, and periodic QRT maps. Later chapters cover these topics and more in detail. While QRT maps will be familiar to specialists in algebraic geometry, the present volume makes the subject accessible to mathematicians and graduate students in a classroom setting or for self-study.

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Page Count

627

Publisher

Springer

Published Date

ISBN 10

1441971165

ISBN 13

9781441971166

Fourier Integral Operators

By: J.J. Duistermaat

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Fourier Integral Operators

By: J.J. Duistermaat

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Page Count

155

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817681086

ISBN 13

9780817681081

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

By: J.J. Duistermaat

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The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

By: J.J. Duistermaat

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245

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Springer Science & Business Media

Published Date

ISBN 10

1461253446

ISBN 13

9781461253440

Distributions

Theory and Applications

By: J.J. Duistermaat,Johan A.C. Kolk

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Distributions

Theory and Applications

By: J.J. Duistermaat,Johan A.C. Kolk

This textbook is an application-oriented 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.

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