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E-raamat: Inverse Spectral Problems for Linear Differential Operators and Their Applications

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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.
Preface vii
Introduction ix
Part I. Recovery of differential operators from the Weyl matrix
Formulation of the inverse problem. A uniqueness theorem
1(12)
Solution of the inverse problem on the half-line
13(23)
Differential operators with a simple spectrum
36(15)
Solution of the inverse problem on a finite interval
51(25)
Inverse problems for the self-adjoint case
76(11)
Differential operators with singularities
87(12)
Part II. Recovery of differential operators from the Weyl functions
Differential operators with a ``separate'' spectrum
99(8)
Stability of the solution of the inverse problem
107(30)
Method of standard models. Information condition
137(17)
An inverse problem of elasticity theory
154(5)
Differential operators with locally integrable coefficients
159(18)
Discrete inverse problems. Applications to differential operators
177(25)
Inverse problems for integro-differential operators
202(17)
Appendix I. Solution of the Boussinesq equation on the half-line by the inverse problem method 219(14)
Appendix II. Integrable dynamical systems connected with higher-order difference operators 233(10)
References 243(8)
Subject index 251