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Author : Harold Widom
Publisher : Springer
ISBN 13 : 3540396411
Total Pages : 155 pages
Book Rating : 4.5/5 (43 download)
Download or read book Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains written by Harold Widom and published by Springer. This book was released on 2006-11-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Heinz O. Cordes
Publisher : Springer
ISBN 13 : 3540478868
Total Pages : 495 pages
Book Rating : 4.5/5 (44 download)
Download or read book Pseudo-Differential Operators written by Heinz O. Cordes and published by Springer. This book was released on 2006-11-15 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : G. Grubb
Publisher : Springer Science & Business Media
ISBN 13 : 1475718985
Total Pages : 520 pages
Book Rating : 4.4/5 (757 download)
Download or read book Functional Calculus of Pseudo-Differential Boundary Problems written by G. Grubb and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: CHAPTER 1. STANDARD PSEUDO-DIFFERENTIAL BOUNDARY PROBLEMS AND THEIR REALIZATIONS 1. 1 Introductory remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2 The calculus of pseudo-differential boundary problems . . •. 19 1. 3 Green's formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1. 4 Realizations and normal boundary conditions . . . . . . . . . . . . . . 39 1. 5 Parameter-ellipticity and parabolicity . . . . . . . . . . . . . . . . . . . 50 1. 6 Adjoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1. 7 Semiboundedness and coerciveness . . . . . . . . •. . . . . . . . . . . •. . . . 96 CHAPTER 2. THE CALCULUS OF PARAMETER-DEPENDENT OPERATORS 2. 1 Parameter-dependent pseudo-differential operators . . •. . . . . 125 2. 2 The transmission property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 2. 3 Parameter-dependent boundary symbol s . . . . . . . . . . . . . . . . . . . . . 179 2. 4 Operators and kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 2. 5 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2. 6 Composition of xn-independent boundary symbol operators . . 234 2. 7 Compositions in general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 2. 8 Strictly homogeneous symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 CHAPTER 3. PARAMETRIX AND RESOLVENT CONSTRUCTIONS 3. 1 Ellipticity. Auxiliary elliptic operators . . . . . . . . . . . . . . . . 280 3. 2 The parametrix construction . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . 297 3. 3 The resolvent of a realization . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 3. 4 Other special cases . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 CHAPTER 4. SOME APPLICATIONS 4. 1 Evolution problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 4. 2 The heat operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4. 3 An index formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 4. 4 Complex powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 4. 5 Spectral asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 4. 6 Implicit eigenvalue problems . . . . . . . . . . . . . . . . . . . . . . . •. . . . . 437 4. 7 Singular perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 APPENDIX. VARIOUS PREREQUISITES (A. 1 General notation. A. 2 Functions and distributions. A. 3 Sobolev spaces. A. 4 Spaces over sub sets of mn. A. 5 Spaces over manifolds. A. 6 Notions from 473 spectral theory. ) '" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . •. . . . . . . •. . . . . . . . . . . . . . . •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Author : Estelle L. Basor
Publisher : Birkhäuser
ISBN 13 : 3034885431
Total Pages : 208 pages
Book Rating : 4.0/5 (348 download)
Download or read book Toeplitz Operators and Related Topics written by Estelle L. Basor and published by Birkhäuser. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Harold Widom, a distinguished mathematician and renowned expert in the area of Toeplitz, Wiener-Hopf and pseudodifferential operators, on the occasion of his sixtieth birthday. The book opens with biographical material and a list of the mathematician's publications, this being followed by two papers based on Toeplitz lectures which he delivered at Tel Aviv University in March, 1993. The rest of the book consists of a selection of papers containing some recent achievements in the following areas: Szegö-Widom asymptotic formulas for determinants of finite sections of Toeplitz matrices and their generalizations, the Fisher-Hartwig conjecture, random matrices, analysis of kernels of Toeplitz matrices, projectional methods and eigenvalue distribution for Toeplitz matrices, the Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorff type theorems. The book will appeal to a wide audience of pure and applied mathematicians.
Author : Estelle Basor
Publisher : Springer Nature
ISBN 13 : 3031138511
Total Pages : 606 pages
Book Rating : 4.0/5 (311 download)
Download or read book Toeplitz Operators and Random Matrices written by Estelle Basor and published by Springer Nature. This book was released on 2023-01-01 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.
Author : Man Wah Wong
Publisher : World Scientific
ISBN 13 : 9789810238131
Total Pages : 156 pages
Book Rating : 4.2/5 (381 download)
Download or read book An Introduction to Pseudo-differential Operators written by Man Wah Wong and published by World Scientific. This book was released on 1999 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new edition of An Introduction to Pseudo-Differential Operators, the style & scope of the original book are retained. A chapter on the interchange of order of differentiation & integration is added at the beginning to make the book more self-contained, & a chapter on weak solutions of pseudo-differential equations is added at the end to enhance the value of the book as a work on partial differential equations. Several chapters are provided with additional exercises. The bibliography is slightly expanded & an index is added. Contents: Differentiation of Integrals Depending on Parameters; The Convolution; The Fourier Transform; Tempered Distributions; Symbols, Pseudo-Differential Operators & Asymptotic Expansions; A Partition of Unity & Taylor's Formula; The Product of Two Pseudo-Differential Operators; The Formal Adjoint of a Pseudo-Differential Operator; The Parametrix of an Elliptic Pseudo-Differential Operator; Lp-Boundedness of Pseudo-Differential Operators, 1
Author : A. Böttcher
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112707192
Total Pages : 512 pages
Book Rating : 4.1/5 (127 download)
Download or read book Analysis of Toeplitz Operators written by A. Böttcher and published by Walter de Gruyter GmbH & Co KG. This book was released on 1989-12-31 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Analysis of Toeplitz Operators".
Author : Albrecht Böttcher
Publisher : Springer Science & Business Media
ISBN 13 : 366202652X
Total Pages : 511 pages
Book Rating : 4.6/5 (62 download)
Download or read book Analysis of Toeplitz Operators written by Albrecht Böttcher and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised introduction to the advanced analysis of block Toeplitz operators including recent research. This book builds on the success of the first edition which has been used as a standard reference for fifteen years. Topics range from the analysis of locally sectorial matrix functions to Toeplitz and Wiener-Hopf determinants. This will appeal to both graduate students and specialists in the theory of Toeplitz operators.
Author : Arsene
Publisher : Birkhäuser
ISBN 13 : 303487698X
Total Pages : 369 pages
Book Rating : 4.0/5 (348 download)
Download or read book Advances in Invariant Subspaces and Other Results of Operator Theory written by Arsene and published by Birkhäuser. This book was released on 2013-11-11 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The annual Operator Theory conferences, organized by the Department of Mathematics of INC REST and the University of Timi?oara, are intended to promote cooperation and exchange of information between specialists in all areas of operator theory. This volume consists of papers contributed by the participants of the 1984 Conference. They reflect a great variety of topics, dealt with by the modern operator theory, including very recent advances in the invariant subspace problem, subalgebras of operator algebras, hyponormal, Hankel and other special classes of operators, spectral decompositions, aspects of dilation theory and so on. The research contracts of the Department of Mathematics of INCREST with the National Council for Science and Technology of Romania provided the means for developing the research activity in mathematics; they represent the generous framework of these meetings, too. It is our pleasure to acknowledge the financial support of UNESCO which also contibuted to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Mariana Bota, Camelia Minculescu and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for the excellent job they did.
Author : Yulia E. Karpeshina
Publisher : American Mathematical Soc.
ISBN 13 : 0821832964
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)
Download or read book Advances in Differential Equations and Mathematical Physics written by Yulia E. Karpeshina and published by American Mathematical Soc.. This book was released on 2003 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the 9th International Conference on Differential Equations and Mathematical Physics. It contains 29 research and survey papers contributed by conference participants. The conference provided researchers a forum to present and discuss their recent results in a broad range of areas encompassing the theory of differential equations and their applications in mathematical physics. Papers in this volume represent some of the most interesting results and the major areas of research that were covered, including spectral theory with applications to non-relativistic and relativistic quantum mechanics, including time-dependent and random potential, resonances, many body systems, pseudodifferential operators and quantum dynamics, inverse spectral and scattering problems, the theory of linear and nonlinear partial differential equations with applications in fluid dynamics, conservation laws and numerical simulations, as well as equilibrium and nonequilibrium statistical mechanics. The volume is intended for graduate students and researchers interested in mathematical physics.
Author : I. Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034892845
Total Pages : 528 pages
Book Rating : 4.0/5 (348 download)
Download or read book Contributions to Operator Theory and its Applications written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nicolas Lerner
Publisher : Springer Science & Business Media
ISBN 13 : 3764385103
Total Pages : 408 pages
Book Rating : 4.7/5 (643 download)
Download or read book Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators written by Nicolas Lerner and published by Springer Science & Business Media. This book was released on 2011-01-30 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H ̈ ormander (Chapter 18 in the book [73]) on this topic.
Author : Mihai Putinar
Publisher : Birkhäuser
ISBN 13 : 3034874669
Total Pages : 295 pages
Book Rating : 4.0/5 (348 download)
Download or read book Lectures on Hyponormal Operators written by Mihai Putinar and published by Birkhäuser. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lectures are based on a course deli vered by the authors at the Uni versi ty of Bucharest, in the winter semester 1985-1986. Without aiming at completeness, the topics selected cover all the major questions concerning hyponormal operators. Our main purpose is to provide the reader with a straightforward access to an active field of research which is strongly related to the spectral and perturbation theories of Hilbert space operators, singular integral equations and scattering theory. We have in view an audience composed especially of experts in operator theory or integral equations, mathematical physicists and graduate students. The book is intended as a reference for the basic results on hyponormal operators, but has the structure of a textbook. Parts of it can also be used as a second year graduate course. As prerequisites the reader is supposed to be acquainted with the basic principles of functional analysis and operator theory as covered for instance by Reed and Simon [1]. A t several stages of preparation of the manuscript we were pleased to benefit from proper comments made by our cOlleagues: Grigore Arsene, Tiberiu Constantinescu, Raul Curto, Jan Janas, Bebe Prunaru, Florin Radulescu, Khrysztof Rudol, Konrad Schmudgen, Florian-Horia Vasilescu. We warmly thank them all. We are indebted to Professor Israel Gohberg, the editor of this series, for his constant encouragement and his valuable mathematical advice. We wish to thank Mr. Benno Zimmermann, the Mathematics Editor at Birkhauser Verlag, for cooperation and assistance during the preparation of the manuscript.
Author : Stefan Hildebrandt
Publisher : Springer
ISBN 13 : 3540460241
Total Pages : 433 pages
Book Rating : 4.5/5 (44 download)
Download or read book Partial Differential Equations and Calculus of Variations written by Stefan Hildebrandt and published by Springer. This book was released on 2006-11-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Author : Svetozar Kurepa
Publisher : Springer
ISBN 13 : 3540478760
Total Pages : 442 pages
Book Rating : 4.5/5 (44 download)
Download or read book Functional Analysis II written by Svetozar Kurepa and published by Springer. This book was released on 2006-11-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a long monographic paper by J. Hoffmann-Jorgensen and a number of shorter research papers and survey articles covering different aspects of functional analysis and its application to probability theory and differential equations.
Author : David Mumford
Publisher : Springer
ISBN 13 : 3662215810
Total Pages : 319 pages
Book Rating : 4.6/5 (622 download)
Download or read book The Red Book of Varieties and Schemes written by David Mumford and published by Springer. This book was released on 2013-11-11 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)
Author : George B. Seligman
Publisher : Springer
ISBN 13 : 3540388648
Total Pages : 203 pages
Book Rating : 4.5/5 (43 download)
Download or read book Constructions of Lie Algebras and their Modules written by George B. Seligman and published by Springer. This book was released on 2006-11-14 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.
