Spectral Theory for Second Order Systems and Indefinite Sturm-Liouville Problems PDF Download
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Author: Carsten Trunk
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Carsten Trunk
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Don Hinton
Publisher: CRC Press
ISBN: 1000657760
Category : Mathematics
Languages : en
Pages : 414
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Book Description
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.
Author: Boris Moiseevich Levitan
Publisher: American Mathematical Soc.
ISBN: 082181589X
Category : Mathematics
Languages : en
Pages : 542
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Book Description
Presents a monograph that is devoted to the spectral theory of the Sturm- Liouville operator and to the spectral theory of the Dirac system. This book concerns with nth order operators that can serve as simply an introduction to this domain. It includes a chapter that discusses this theory.
Author: L.A. Sakhnovich
Publisher: Birkhäuser
ISBN: 3034887132
Category : Mathematics
Languages : en
Pages : 201
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Book Description
Theorems of factorising matrix functions and the operator identity method play an essential role in this book in constructing the spectral theory (direct and inverse problems) of canonical differential systems. Includes many varied applications of the general theory.
Author: Vacheslav A. Yurko
Publisher: Walter de Gruyter
ISBN: 3110940965
Category : Mathematics
Languages : en
Pages : 316
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Book Description
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 science. This monograph is devoted to inverse problems of spectral analysis for ordinary differential equations. Its aim ist to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory. The book consists of three chapters: In Chapter 1 the method of spectral mappings is presented in the simplest version for the Sturm-Liouville operator. In Chapter 2 the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval, is considered. In Chapter 3 inverse spectral problems for differential operators with nonlinear dependence on the spectral parameter are studied.
Author:
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Category :
Languages : en
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This report contains the proceedings of the workshop which was held at Argonne during the period May 14 through June 15, 1984. The report contains 22 articles, authored or co-authored by the participants in the workshop. Topics covered at the workshop included the asymptotics of eigenvalues and eigenfunctions; qualitative and quantitative aspects of Sturm-Liouville eigenvalue problems with discrete and continuous spectra; polar, indefinite, and nonselfadjoint Sturm-Liouville eigenvalue problems; and systems of differential equations of Sturm-Liouville type.
Author: Christian Remling
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110563231
Category : Mathematics
Languages : en
Pages : 206
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Book Description
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
Author: Andreas Fleige
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 150
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Book Description
The vibration of a string with a (nondecreasing) mass distribution function m leads to a generalized differential equation of second order, introduced by Krein and by Feller. The author allows also nonmonotonic functions m and hence, gets into the theory of indefinite inner product spaces. Here at the first time a systematic presentation of the generalized differential expression and of J-selfadjoint operator realizations is given. Developing a spectral theory for such Krein-Feller operators, the author derives the most general known criteria for the regularity of the critical point infinity. Then, by specialization, expansion theorems for wide classes of indefinite second order differential and difference operators are obtained.
Author: Andrei Giniatoulline
Publisher: R.T. Edwards, Inc.
ISBN: 9781930217096
Category : Mathematics
Languages : en
Pages : 212
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Book Description
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.
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.
