Recent Developments in Sturm-Liouville Theory PDF Download

Author: Anton Zettl
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110719002
Category : Mathematics
Languages : en
Pages : 262

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Book Description
This book provides a modern survey of some basic properties of Sturm-Liouville problems and to bring the reader to the forefront of knowledge of some areas of the theory. For example, some special Sturm-Liouville eigenvalue problems are equivalent to certain Jacobi and cyclic Jacobi matrix eigenvalue problems. A new approach to problems with periodic conditions is developed.

Author: Anton Zettl
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311071938X
Category : Mathematics
Languages : en
Pages : 236

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Book Description
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.

Author: Werner O. Amrein
Publisher: Springer Science & Business Media
ISBN: 3764373598
Category : Mathematics
Languages : en
Pages : 348

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Book Description
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.

Author: Werner O. Amrein
Publisher: Springer Science & Business Media
ISBN: 9783764370664
Category : Mathematics
Languages : en
Pages : 364

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Book Description
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.

Author: Anton Zettl
Publisher: American Mathematical Soc.
ISBN: 0821852671
Category : Education
Languages : en
Pages : 346

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Book Description
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.

Author: Vladislav V. Kravchenko
Publisher: Birkhäuser
ISBN: 9783030478483
Category : Mathematics
Languages : en
Pages : 154

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Book Description
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.

Author: Yiu-Chung Hon
Publisher: World Scientific
ISBN: 9812383662
Category : Science
Languages : en
Pages : 473

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Book Description
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.

Author: Mohammed Al-Gwaiz
Publisher: Springer Science & Business Media
ISBN: 1846289718
Category : Mathematics
Languages : en
Pages : 270

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Book Description
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.

Author: F.V. Atkinson
Publisher: CRC Press
ISBN: 1439816239
Category : Mathematics
Languages : en
Pages : 297

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Book Description
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

Author: Vladimir Aleksandrovich Marchenko
Publisher: American Mathematical Soc.
ISBN: 0821853163
Category : Mathematics
Languages : en
Pages : 410

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Book Description
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.