Spectral Theory of Ordinary Differential Operators

2006-11-15

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.

Author: Joachim Weidmann

Publisher: Springer

ISBN: 9783540479123

Category: Mathematics

Page: 304

View: 161

Download →

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.
Posted in:

Spectral and Scattering Theory for Ordinary Differential Equations

2020-10-27

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.

Author: Christer Bennewitz

Publisher: Springer Nature

ISBN: 9783030590888

Category: Mathematics

Page: 379

View: 609

Download →

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.
Posted in:

Spectral Theory and Differential Equations

2014-09-26

MR0032067 (11:248e) B. M. Levitan, Determination of a Sturm-Liouville differential equation in terms of two spectra, ... MR2158108 (2006b:34023) J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Academic Press, Boston, 1987.

Author: E. Khruslov

Publisher: American Mathematical Society

ISBN: 9781470416836

Category: Mathematics

Page: 251

View: 961

Download →

This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in that broad spectrum of areas.
Posted in:

Spectral Theory and Differential Equations

2006-11-15

Scattering theory for differential operators. I operator theory, II self-adjoint elliptic operators. J. Math a Soc. Japan 25, 75–10k and 222–234 (1973). 17. Schechter, M. : Spectra of partial differential operators.

Author: W.N. Everitt

Publisher: Springer

ISBN: 9783540374442

Category: Mathematics

Page: 326

View: 310

Download →

Posted in:

Spectral Theory and Differential Operators

2018-05-03

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 ...

Author: David Edmunds

Publisher: Oxford University Press

ISBN: 9780192540102

Category: Mathematics

Page:

View: 134

Download →

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.
Posted in: