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Author : Anonim
Publisher : Elsevier
Page : 209 pages
File Size : 40,9 Mb
Release : 2011-09-21
Category : Mathematics
ISBN : 0080871240
Spectral Theory and Asymptotics of Differential Equations
Author : Eduardus Marie de Jager
Publisher : Unknown
Page : 208 pages
File Size : 55,9 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:251905240
Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 46,7 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:1400498277
Author : E. M. de Jager
Publisher : Unknown
Page : 208 pages
File Size : 52,7 Mb
Release : 1974
Category : Asymptotic Expansions Congresses
ISBN : LCCN:10097243
Author : Scheveningen Conference on Differential Equations
Publisher : Unknown
Page : 85 pages
File Size : 46,5 Mb
Release : 1974
Category : Vector spaces
ISBN : 0720427002
Author : Sebastian Klein
Publisher : Springer
Page : 326 pages
File Size : 51,9 Mb
Release : 2018-12-05
Category : Mathematics
ISBN : 9783030012762
This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.
Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 346 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882316
The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.
Author : Victor Ivrii
Publisher : Springer Science & Business Media
Page : 736 pages
File Size : 45,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662124963
The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl's conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.
Author : Fedor S. Rofe-Beketov,Aleksandr M. Khol'kin,Ognjen Milatovic
Publisher : World Scientific
Page : 466 pages
File Size : 50,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812703453
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."
Author : Michael Demuth,Bert-Wolfgang Schulze,Ingo Witt
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 50,8 Mb
Release : 2011-02-01
Category : Mathematics
ISBN : 9783034800242
This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.
Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 48,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662067192
This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including 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".
Author : David Holcman,Zeev Schuss
Publisher : Springer
Page : 444 pages
File Size : 46,6 Mb
Release : 2018-05-25
Category : Mathematics
ISBN : 9783319768953
This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.
Author : Johannes Sjöstrand
Publisher : Springer
Page : 496 pages
File Size : 41,5 Mb
Release : 2019-05-17
Category : Mathematics
ISBN : 9783030108199
The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Author : Boris Moiseevich Levitan,Ishkhan Saribekovich Sargsi͡an
Publisher : American Mathematical Soc.
Page : 525 pages
File Size : 51,5 Mb
Release : 1975
Category : Mathematics
ISBN : 9780821815892
This monograph is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. In addition, some results are given for nth order ordinary differential operators. Those parts of this book which concern nth order operators can serve as simply an introduction to this domain, which at the present time has already had time to become very broad. For the convenience of the reader who is not familar with abstract spectral theory, the authors have inserted a chapter (Chapter 13) in which they discuss this theory, concisely and in the main without proofs, and indicate various connections with the spectral theory of differential operators.
Author : Christer Bennewitz,Malcolm Brown,Rudi Weikard
Publisher : Springer Nature
Page : 379 pages
File Size : 44,9 Mb
Release : 2020-10-27
Category : Mathematics
ISBN : 9783030590888
This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm–Liouville equations. Sturm–Liouville theory has applications in partial differential equations and mathematical physics. Examples include classical PDEs such as the heat and wave equations. Written by leading experts, this book provides a modern, systematic treatment of the theory. The main topics are the spectral theory and eigenfunction expansions for Sturm–Liouville equations, as well as scattering theory and inverse spectral theory. It is the first book offering a complete account of the left-definite theory for Sturm–Liouville equations. The modest prerequisites for this book are basic one-variable real analysis, linear algebra, as well as an introductory course in complex analysis. More advanced background required in some parts of the book is completely covered in the appendices. With exercises in each chapter, the book is suitable for advanced undergraduate and graduate courses, either as an introduction to spectral theory in Hilbert space, or to the spectral theory of ordinary differential equations. Advanced topics such as the left-definite theory and the Camassa–Holm equation, as well as bibliographical notes, make the book a valuable reference for experts.
