Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91
Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91

Author: Lars Hörmander

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 296

ISBN-13: 1400881587

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Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.

Seminar on Singularities of Solutions of Linear Partial Differential Equations
Seminar on Singularities of Solutions of Linear Partial Differential Equations

Author: George F. Oster

Publisher: Princeton University Press

Published: 1978

Total Pages: 295

ISBN-13: 0691082138

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Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.

The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99
The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99

Author: L. Boutet de Monvel

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 166

ISBN-13: 1400881447

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The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

Essays in Mathematics and its Applications
Essays in Mathematics and its Applications

Author: Themistocles M. Rassias

Publisher: Springer

Published: 2016-06-14

Total Pages: 659

ISBN-13: 331931338X

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This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.

The Mathematical Legacy of Leon Ehrenpreis
The Mathematical Legacy of Leon Ehrenpreis

Author: Irene Sabadini

Publisher: Springer Science & Business Media

Published: 2012-04-23

Total Pages: 391

ISBN-13: 8847019478

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Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators.

Partial Differential Equations
Partial Differential Equations

Author: M. S. Agranovich

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 292

ISBN-13: 9780821833032

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Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplecticgeometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and general unbounded domains, linear elliptic problems with a parameter for mixed order systems, infinite-dimensional Schrodinger equations, Navier-Stokes equations, and nonlinear Maxwellequations. The book ends on a historical note with a paper about Vishik's seminar as a whole and a list of selected talks given from 1964 through 1989. The book is suitable for graduate students and researchers in pure and applied mathematics and mathematical physics.