Sturm-Liouville theory
著者
書誌事項
Sturm-Liouville theory
（Mathematical surveys and monographs, v. 121）
American Mathematical Society, c2005
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注記
Includes bibliographical references (p. 303-326) and index
内容説明・目次
内容説明
In 1836 and 1837, Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which began the subject now known as the Sturm-Liouville theory. In 1910, Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, Sturm-Liouville theory has remained an intensely active field of research with many applications in mathematics and mathematical physics. The purpose of the present book is to provide a modern survey of some of the basic properties of Sturm-Liouville theory and to bring the reader to the forefront of research on some aspects of this theory.Prerequisites for using the book are a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory. The book has an extensive list of references and examples and numerous open problems. Examples include classical equations and functions associated with Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, and Morse; also included are examples associated with the harmonic oscillator and the hydrogen atom.
Many special functions of applied mathematics and mathematical physics occur in these examples. This book offers a well-organized viewpoint on some basic features of Sturm-Liouville theory. With many useful examples treated in detail, it will make a fine independent study text and is suitable for graduate students and researchers interested in differential equations.
目次
Part 1. Existence and uniqueness problems: First order systems Scalar initial value problems Part 2. Regular boundary value problems: Two-point regular boundary value problems Regular self-adjoint problems Regular left-definite and indefinite problems Part 3. Oscillation and singular existence problems: Oscillation The limit-point, limit-circle dichotomy Singular initial value problems Part 4. Singular boundary value problems: Two-point singular boundary value problems Singular self-adjoint problems Singular indefinite problems Singular left-definite problems Part 5. Examples and other topics: Two intervals Examples Notation Comments on some topics not covered Open problems Bibliography Index.
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