Spectral Theory And Differential Equations

Author : Joachim Weidmann
Publisher : Springer
Page : 310 pages
File Size : 52,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540479123

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Spectral Theory of Ordinary Differential Operators by Joachim Weidmann Pdf

These notes will be useful and of interest to mathematicians and physicists active in research as well as for students with some knowledge of the abstract theory of operators in Hilbert spaces. They give a complete spectral theory for ordinary differential expressions of arbitrary order n operating on -valued functions existence and construction of self-adjoint realizations via boundary conditions, determination and study of general properties of the resolvent, spectral representation and spectral resolution. Special attention is paid to the question of separated boundary conditions, spectral multiplicity and absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville operators and Dirac systems) the classical theory of Weyl-Titchmarch is included. Oscillation theory for Sturm-Liouville operators and Dirac systems is developed and applied to the study of the essential and absolutely continuous spectrum. The results are illustrated by the explicit solution of a number of particular problems including the spectral theory one partical Schrödinger and Dirac operators with spherically symmetric potentials. The methods of proof are functionally analytic wherever possible.

Author : David Eric Edmunds,W. D. Evans
Publisher : Oxford University Press
Page : 610 pages
File Size : 45,5 Mb
Release : 2018
Category : Mathematics
ISBN : 9780198812050

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Spectral Theory and Differential Operators by David Eric Edmunds,W. D. Evans Pdf

This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.--

Author : Fedor S. Rofe-Beketov,Aleksandr M. Khol'kin,Ognjen Milatovic
Publisher : World Scientific
Page : 466 pages
File Size : 45,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812703453

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Spectral Analysis of Differential Operators by Fedor S. Rofe-Beketov,Aleksandr M. Khol'kin,Ognjen Milatovic Pdf

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 Stephen Patrick Eastham
Publisher : Unknown
Page : 148 pages
File Size : 40,9 Mb
Release : 1973
Category : Differential equations
ISBN : UOM:39015058965974

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The Spectral Theory of Periodic Differential Equations by Michael Stephen Patrick Eastham Pdf

Author : David Edmunds,Des Evans
Publisher : Oxford University Press
Page : 128 pages
File Size : 41,5 Mb
Release : 2018-05-03
Category : Mathematics
ISBN : 9780192540102

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Spectral Theory and Differential Operators by David Edmunds,Des Evans Pdf

This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

Author : Michael Demuth,Bert-Wolfgang Schulze
Publisher : Birkhäuser
Page : 346 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882316

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Partial Differential Equations and Spectral Theory by Michael Demuth,Bert-Wolfgang Schulze Pdf

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 : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 55,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662067192

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Partial Differential Equations VII by M.A. Shubin Pdf

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 : Anonim
Publisher : Elsevier
Page : 209 pages
File Size : 45,5 Mb
Release : 2011-09-21
Category : Mathematics
ISBN : 0080871240

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Spectral Theory and Asymptotics of Differential Equations by Anonim Pdf

Spectral Theory and Asymptotics of Differential Equations

Author : W. N. Everitt
Publisher : Unknown
Page : 340 pages
File Size : 55,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366217135X

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Spectral Theory and Differential Equations by W. N. Everitt Pdf

Author : Christer Bennewitz,Malcolm Brown,Rudi Weikard
Publisher : Springer Nature
Page : 379 pages
File Size : 46,5 Mb
Release : 2020-10-27
Category : Mathematics
ISBN : 9783030590888

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Spectral and Scattering Theory for Ordinary Differential Equations by Christer Bennewitz,Malcolm Brown,Rudi Weikard Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 49,7 Mb
Release : 1991
Category : Differential equations, Partial
ISBN : 0387546774

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Partial Differential Equations by Anonim Pdf

Author : W.N. Everitt
Publisher : Springer
Page : 338 pages
File Size : 43,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540374442

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Spectral Theory and Differential Equations by W.N. Everitt Pdf

Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 198 pages
File Size : 50,9 Mb
Release : 1995
Category : Mathematics
ISBN : 0521587107

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Spectral Theory and Differential Operators by E. Brian Davies Pdf

This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.

Author : D. E. Edmunds,W.D. Evans
Publisher : Springer
Page : 322 pages
File Size : 54,8 Mb
Release : 2018-11-20
Category : Mathematics
ISBN : 9783030021252

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Elliptic Differential Operators and Spectral Analysis by D. E. Edmunds,W.D. Evans Pdf

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.

Author : E. B. Davies
Publisher : Cambridge University Press
Page : 212 pages
File Size : 48,8 Mb
Release : 1989
Category : Mathematics
ISBN : 0521409977

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Heat Kernels and Spectral Theory by E. B. Davies Pdf

Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.