Elliptic Differential Operators And Spectral Analysis

Author : D. E. Edmunds,W.D. Evans
Publisher : Springer
Page : 322 pages
File Size : 55,6 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 : Youri Egorov,Vladimir A. Kondratiev
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 48,6 Mb
Release : 1996-07-30
Category : Mathematics
ISBN : 3764353902

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On Spectral Theory of Elliptic Operators by Youri Egorov,Vladimir A. Kondratiev Pdf

It is well known that a wealth of problems of different nature, applied as well as purely theoretic, can be reduced to the study of elliptic equations and their eigen-values. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view. This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential equations. The reader will find hardly any intersections with the books of Shubin [Sh] or Rempel-Schulze [ReSch] or with the works cited there. This book also has no general information in common with the books by Egorov and Shubin [EgShu], which also deal with spectral properties of elliptic operators. There is nothing here on oblique derivative problems; the reader will meet no pseudodifferential operators. The main subject of the book is the estimates of eigenvalues, especially of the first one, and of eigenfunctions of elliptic operators. The considered problems have in common the approach consisting of the application of the variational principle and some a priori estimates, usually in Sobolev spaces. In many cases, impor tant for physics and mechanics, as well as for geometry and analysis, this rather elementary approach allows one to obtain sharp results.

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

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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 : Yuri V Egorov,Vladimir A Kondratiev
Publisher : Unknown
Page : 346 pages
File Size : 47,5 Mb
Release : 1996-07-30
Category : Electronic
ISBN : 3034890303

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On Spectral Theory of Elliptic Operators by Yuri V Egorov,Vladimir A Kondratiev Pdf

Author : Bernhelm Booss,Krzysztof P. Wojciechowski
Publisher : World Scientific
Page : 553 pages
File Size : 40,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812773609

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Analysis, Geometry and Topology of Elliptic Operators by Bernhelm Booss,Krzysztof P. Wojciechowski Pdf

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.

Author : M.A. Shubin
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 42,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642565793

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Pseudodifferential Operators and Spectral Theory by M.A. Shubin Pdf

I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.

Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 198 pages
File Size : 42,8 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 : Jaures Cecconi
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 44,8 Mb
Release : 2011-06-04
Category : Mathematics
ISBN : 9783642109553

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Spectral Analysis by Jaures Cecconi Pdf

G. Bottaro: Quelques résultats d’analyse spectrale pour des opérateurs différentiels à coefficients constants sur des domaines non bornés.- L. Gårding: Eigenfuction expansions.- C. Goulaouic: Valeurs propres de problèmes aux limites irréguliers: applications.- G. Grubb: Essential spectra of elliptic systems on compact manifolds.- J.Cl. Guillot: Quelques résultats récents en Scattering.- N. Schechter: Theory of perturbations of partial differential operators.- C.H. Wilcox: Spectral analysis of the Laplacian with a discontinuous coefficient.

Author : David Edmunds,Des Evans
Publisher : Oxford University Press
Page : 128 pages
File Size : 45,5 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 : Victor Ivrii
Publisher : Springer
Page : 244 pages
File Size : 50,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540389118

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Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds with Boundary by Victor Ivrii Pdf

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Author : Michael Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 41,6 Mb
Release : 2014-01-18
Category : Mathematics
ISBN : 9783319025506

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Fourier Analysis by Michael Ruzhansky,Ville Turunen Pdf

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”

Author : Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong
Publisher : Birkhäuser
Page : 236 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878401

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Advances in Pseudo-Differential Operators by Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong Pdf

This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Author : Andrei Giniatoulline
Publisher : R.T. Edwards, Inc.
Page : 212 pages
File Size : 47,8 Mb
Release : 2005
Category : Mathematics
ISBN : 1930217099

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An Introduction to Spectral Theory by Andrei Giniatoulline Pdf

A brief and accessible introduction to the spectral theory of linear second order elliptic differential operators. By introducing vital topics of abstract functional analysis where necessary, and using clear and simple proofs, the book develops an elegant presentation of the theory while integrating applications of basic real world problems involving the Laplacian. Suitable for use as a self-contained introduction for beginners or as a one-semester student text; contains some 25 examples and 60 exercises, most with detailed hints.

Author : Mikhail A. Shubin
Publisher : Springer
Page : 0 pages
File Size : 53,7 Mb
Release : 1987
Category : Mathematics
ISBN : 3642968546

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Pseudodifferential Operators and Spectral Theory by Mikhail A. Shubin Pdf

The theory of pseudo differential operators (abbreviated PD~) is compara tively young; in its modern form it was created in the mid-sixties. The progress achieved with its help, however, has been so essential that without PD~ it would indeed be difficult to picture modern analysis and mathematical physics. PD~ are of particular importance in the study of elliptic equations. Even the simplest operations on elliptic operators (e. g. taking the inverse or the square root) lead out of the class of differential operators but will, under reasonable assumptions, preserve the class of PD~. A significant role is played by PD~ in the index theory for elliptic operators, where PD~ are needed to extend the class of possible deformations of an operator. PD~ appear naturally in the reduction to the boundary for any elliptic boundary problem. In this way, PD~ arise not as an end-in-themselves, but as a powerful and natural tool for the study of partial differential operators (first and foremost elliptic and hypo elliptic ones). In many cases, PD~ allow us not only to establish new theorems but also to have a fresh look at old ones and thereby obtain simpler and more transparent formulations of already known facts. This is, for instance, the case in the theory of Sobolev spaces. A natural generalization of PD~ are the Fourier integral operators (abbreviatedFIO), the first version ofwhich was the Maslov canonical operator.

Author : Yuri V. Egorov,Vladimir Kondratiev
Publisher : Unknown
Page : 328 pages
File Size : 54,6 Mb
Release : 1991
Category : Electronic
ISBN : OCLC:637665200

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On Spectral Theory of Elliptic Operators by Yuri V. Egorov,Vladimir Kondratiev Pdf