Inverse spectral problems for differential operators and their applications
著者
書誌事項
Inverse spectral problems for differential operators and their applications
（Analytical methods and special functions, v. 2）
Gordon & Breach, c2000
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注記
Includes bibliographical references (p. 243-249) and index
内容説明・目次
内容説明
Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spectrum is arbitrary. The Weyl matrix is introduced and studied as a spectral characteristic. The second part of the book is devoted to solving incomplete inverse problems when a priori information about the operator or its spectrum is available and these problems are significant in applications.
目次
- Part One: Recovery of Differential Operators from the Weyl Matrix
- 1. Formulation of the Inverse Problem: A Uniqueness Theorem 2. Solution of the Inverse Problem on the Half-line 3. Differential Operators with a Simple Spectrum 4. Solution of the Inverse Problem on a Finite Interval 5. Inverse Problems for the Self-Adjoint Case 6. Differential Operators with Singularities
- Part Two: Recovery of Differential Operators from the Weyl Functions: Differential Operators with a "Separate Spectrum"
- 7. Stability of the Solution of the Inverse Problem 8.Method of Standard Models: Information Conditions 9. An Inverse Problem of Elasticity Theory 10. Differential Operator with Locally Integrable Coefficients 11. Discrete Inverse Problems: Applications to Differential Operators 12. Inverse Problems for Integro-differential Operators
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