Sturm?Liouville Operators, Their Spectral Theory, and Some Applications
Sturm?Liouville Operators, Their Spectral Theory, and Some Applications

Author: Fritz Gesztesy

Publisher: American Mathematical Society

Published: 2024-09-24

Total Pages: 946

ISBN-13: 1470476665

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This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.

Sturm-Liouville Operators and Applications
Sturm-Liouville Operators and Applications

Author: Vladimir Aleksandrovich Marchenko

Publisher: American Mathematical Soc.

Published: 2011-04-27

Total Pages: 410

ISBN-13: 0821853163

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The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. This book aims to show what can be achieved with the aid of transformation operators in spectral theory as well as their applications.

Sturm-Liouville Theory
Sturm-Liouville Theory

Author: Werner O. Amrein

Publisher: Springer Science & Business Media

Published: 2005-12-05

Total Pages: 348

ISBN-13: 3764373598

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This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.

Spectral Theory & Computational Methods of Sturm-Liouville Problems
Spectral Theory & Computational Methods of Sturm-Liouville Problems

Author: Don Hinton

Publisher: CRC Press

Published: 1997-05-06

Total Pages: 422

ISBN-13: 9780824700300

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Presenting the proceedings of the conference on Sturm-Liouville problems held in conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee, Knoxville, this text covers both qualitative and computational theory of Sturm-Liouville problems. It surveys questions in the field as well as describing applications and concepts.

Spectral Theory of Canonical Systems
Spectral Theory of Canonical Systems

Author: Christian Remling

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-08-21

Total Pages: 244

ISBN-13: 3110562286

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Canonical systems occupy a central position in the spectral theory of second order differential operators. They may be used to realize arbitrary spectral data, and the classical operators such as Schrödinger, Jacobi, Dirac, and Sturm-Liouville equations can be written in this form. ‘Spectral Theory of Canonical Systems’ offers a selfcontained and detailed introduction to this theory. Techniques to construct self-adjoint realizations in suitable Hilbert spaces, a modern treatment of de Branges spaces, and direct and inverse spectral problems are discussed. Contents Basic definitions Symmetric and self-adjoint relations Spectral representation Transfer matrices and de Branges spaces Inverse spectral theory Some applications The absolutely continuous spectrum

An Introduction to Spectral Theory
An Introduction to Spectral Theory

Author: Andrei Giniatoulline

Publisher: R.T. Edwards, Inc.

Published: 2005

Total Pages: 212

ISBN-13: 9781930217096

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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.

Inverse Sturm-Liouville Problems
Inverse Sturm-Liouville Problems

Author: Boris Moiseevič Levitan

Publisher: VSP

Published: 1987

Total Pages: 258

ISBN-13: 9789067640558

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The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.

Inverse Sturm-Liouville Problems and Their Applications
Inverse Sturm-Liouville Problems and Their Applications

Author: G. Freiling

Publisher: Nova Biomedical Books

Published: 2001

Total Pages: 324

ISBN-13:

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This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.

Spectral Theory and Its Applications
Spectral Theory and Its Applications

Author: Bernard Helffer

Publisher: Cambridge University Press

Published: 2013-01-17

Total Pages: 263

ISBN-13: 110703230X

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Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

Jacobi Operators and Completely Integrable Nonlinear Lattices
Jacobi Operators and Completely Integrable Nonlinear Lattices

Author: Gerald Teschl

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 373

ISBN-13: 0821819402

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This volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.