Spectral Theory of Ordinary Differential Operators


Author: Joachim Weidmann
Publisher: Springer
ISBN: 3540479120
Category: Mathematics
Page: 304
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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.

Spectral Theory and Mathematical Physics: Ergodic Schrödinger operators, singular spectrum, orthogonal polynomials, and inverse spectral theory


Author: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 0821842498
Category: Mathematics
Page: 948
View: 5106
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This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to a particular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random and Ergodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensive introduction into an area covered in this volume.

Spectral Theory of Differential Operators


Author: I.W. Knowles,R.T. Lewis
Publisher: Elsevier
ISBN: 9780080871660
Category: Mathematics
Page: 383
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Spectral Theory of Differential Operators

Spectral Theory of Linear Differential Operators and Comparison Algebras


Author: Heinz Otto Cordes
Publisher: Cambridge University Press
ISBN: 0521284430
Category: Mathematics
Page: 342
View: 8835
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The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The author then introduces comparison algebras and describes their theory in L2-spaces and L2-Soboler spaces, and in particular their importance in solving functional analytic problems involving differential operators. The book is based on lectures given in Sweden and the USA.

Degenerate Differential Equations in Banach Spaces


Author: Angelo Favini,Atsushi Yagi
Publisher: CRC Press
ISBN: 9780824716776
Category: Mathematics
Page: 336
View: 7198
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This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

Spectral Theory and Asymptotics of Differential Equations

Proceedings of the Scheveningen Conference on Differential Equations, the Netherlands
Author: N.A
Publisher: Elsevier
ISBN: 9780080871240
Category: Mathematics
Page: 209
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Spectral Theory and Asymptotics of Differential Equations

Spectral Theory and Differential Operators


Author: David Edmunds,Des Evans
Publisher: Oxford University Press
ISBN: 0198812051
Category: Mathematics
Page: 624
View: 4869
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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.

Partial Differential Equations II

Qualitative Studies of Linear Equations
Author: Michael E. Taylor
Publisher: Springer Science & Business Media
ISBN: 9781441970527
Category: Mathematics
Page: 614
View: 897
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This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.

Spectral Theory and Differential Equations

Proceedings of the Symposium held at Dundee, Scotland, July 1-19, 1974
Author: W.N. Everitt
Publisher: Springer
ISBN: 3540374442
Category: Mathematics
Page: 326
View: 6830
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Spectral Theory and Differential Operators


Author: E. Brian Davies,Edward Brian Davies
Publisher: Cambridge University Press
ISBN: 9780521587105
Category: Mathematics
Page: 182
View: 9757
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In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.

Spectral theory of ordinary differential operators


Author: Erich Müller-Pfeiffer
Publisher: N.A
ISBN: 9780853121893
Category: Mathematics
Page: 246
View: 5090
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Pseudodifferential Operators and Spectral Theory


Author: M.A. Shubin
Publisher: Springer Science & Business Media
ISBN: 9783540411956
Category: Mathematics
Page: 288
View: 8283
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This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.

The Spectral Theory of Fourth-order Ordinary Differential Operators


Author: Ellis Rogers von Eschen
Publisher: N.A
ISBN: N.A
Category: Differential equations
Page: 56
View: 7440
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Grundzüge der modernen Analysis


Author: Jean Dieudonné
Publisher: Springer-Verlag
ISBN: 3322900096
Category: Mathematics
Page: 372
View: 3090
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Periodic Differential Operators


Author: B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt
Publisher: Springer Science & Business Media
ISBN: 3034805284
Category: Mathematics
Page: 220
View: 4352
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Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Spectral Theory of Indefinite Krein-Feller Differential Operators


Author: Andreas Fleige
Publisher: Wiley-VCH
ISBN: N.A
Category: Mathematics
Page: 134
View: 5416
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The vibration of a string with a (nondecreasing) mass distribution function m leads to a generalized differential equation of second order, introduced by Krein and by Feller. The author allows also nonmonotonic functions m and hence, gets into the theory of indefinite inner product spaces. Here at the first time a systematic presentation of the generalized differential expression and of J-selfadjoint operator realizations is given. Developing a spectral theory for such Krein-Feller operators, the author derives the most general known criteria for the regularity of the critical point infinity. Then, by specialization, expansion theorems for wide classes of indefinite second order differential and difference operators are obtained.

Lecture Notes in Mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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Spectral Theory of Operators in Hilbert Space


Author: Kurt O. Friedrichs
Publisher: Springer Science & Business Media
ISBN: 1461263964
Category: Mathematics
Page: 245
View: 4820
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The present lectures intend to provide an introduction to the spectral analysis of self-adjoint operators within the framework of Hilbert space theory. The guiding notion in this approach is that of spectral representation. At the same time the notion of function of an operator is emphasized. The formal aspects of these concepts are explained in the first two chapters. Only then is the notion of Hilbert space introduced. The following three chapters concern bounded, completely continuous, and non-bounded operators. Next, simple differential operators are treated as operators in Hilbert space, and the final chapter deals with the perturbation of discrete and continuous spectra. The preparation of the original version of these lecture notes was greatly helped by the assistance of P. Rejto. Various valuable suggestions made by him and by R. Lewis have been incorporated. The present version of the notes contains extensive modifica tions, in particular in the chapters on bounded and unbounded operators. February, 1973 K.O.F. PREFACE TO THE SECOND PRINTING The second printing (1980) is a basically unchanged reprint in which a number of minor errors were corrected. The author wishes to thank Klaus Schmidt (Lausanne) and John Sylvester (New York) for their lists of errors. v TABLE OF CONTENTS I. Spectral Representation 1 1. Three typical problems 1 12 2. Linear space and functional representation.

Ordinary Differential Equations and Operators

A Tribute to F.V. Atkinson. Proceedings of a Symposium held at Dundee, Scotland, March - July 1982
Author: W.N. Everitt,R.T. Lewis
Publisher: Springer
ISBN: 3540386890
Category: Mathematics
Page: 524
View: 5511
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Semigroups of Operators and Spectral Theory


Author: S Kantorovitz
Publisher: CRC Press
ISBN: 9780582277786
Category: Mathematics
Page: 152
View: 1793
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This book presents some aspects of the theory of semigroups of operators, mostly from the point of view of its interaction withspectral theory. In order to make it self-contained, a concise description of the basic theory of semigroups, with complete proofs, is included in Part I. Some of the author's recent results, such as the construction of the Hille-Yosida space for general operators, the semi-simplicity manifold, and a Taylor formula for semigroups as functions of their generator, are also included in Part I. Part II describes recent generalizations (most of them in bookform for the first time), including pre-semigroups, semi-simplicity manifolds in situations more general than that considered in Part I, semigroups of unbounded symmetric operators, and an analogous result on "local cosine families" and semi-analytic vectors. It is hoped that this book will inspire more research in this field. This book will be of particular interest to graduate students and researchers working operator theory and its applications.