Recent Developments in Sturm-Liouville Theory

Recent Developments in Sturm-Liouville Theory
Author: Anton Zettl
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 236
Release: 2021-02-22
Genre: Mathematics
ISBN: 311071938X

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Sturm-Liouville Theory

Sturm-Liouville Theory
Author: Werner O. Amrein
Publisher: Springer Science & Business Media
Total Pages: 348
Release: 2005-12-05
Genre: Mathematics
ISBN: 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.

Sturm-Liouville Theory

Sturm-Liouville Theory
Author: Anton Zettl
Publisher: American Mathematical Soc.
Total Pages: 346
Release: 2005
Genre: Education
ISBN: 0821852671

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In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.

Sturm-Liouville Theory

Sturm-Liouville Theory
Author: Werner O. Amrein
Publisher: Birkhäuser
Total Pages: 336
Release: 2009-09-03
Genre: Mathematics
ISBN: 9783764390228

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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.

Direct and Inverse Sturm-Liouville Problems

Direct and Inverse Sturm-Liouville Problems
Author: Vladislav V. Kravchenko
Publisher: Birkhäuser
Total Pages: 154
Release: 2020-08-18
Genre: Mathematics
ISBN: 9783030478483

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This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Multiparameter Eigenvalue Problems

Multiparameter Eigenvalue Problems
Author: F.V. Atkinson
Publisher: CRC Press
Total Pages: 297
Release: 2010-12-07
Genre: Mathematics
ISBN: 1439816239

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One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problem

Sturm-Liouville Theory and its Applications

Sturm-Liouville Theory and its Applications
Author: Mohammed Al-Gwaiz
Publisher: Springer Science & Business Media
Total Pages: 270
Release: 2008-01-15
Genre: Mathematics
ISBN: 1846289718

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Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The text’s presentation follows a clear, rigorous mathematical style that is highly readable. The author first establishes the basic results of Sturm-Liouville theory and then provides examples and applications to illustrate the theory. The final two chapters, on Fourier and Laplace transformations, demonstrate the use of the Fourier series method for representing functions to integral representations.

Sturm-Liouville Operators and Applications

Sturm-Liouville Operators and Applications
Author: Vladimir Aleksandrovich Marchenko
Publisher: American Mathematical Soc.
Total Pages: 410
Release: 2011-04-27
Genre: Mathematics
ISBN: 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.

Recent Development in Theories & Numerics

Recent Development in Theories & Numerics
Author: Yiu-Chung Hon
Publisher: World Scientific
Total Pages: 473
Release: 2003
Genre: Science
ISBN: 9812383662

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Annotation. Proceedings from the First International Conference on Inverse Problems, Recent Theoretical Development and Numerical Approaches, held at the City University of Hong Kong from January 9-12, 2002.

Direct and Inverse Sturm-Liouville Problems

Direct and Inverse Sturm-Liouville Problems
Author: Vladislav V. Kravchenko
Publisher: Springer Nature
Total Pages: 155
Release: 2020-07-28
Genre: Mathematics
ISBN: 3030478491

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This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.