http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Inverse spectral problems for linear differential operators and their applications
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.
chapter 1 Formulation of the inverse problem. A uniqueness theorem -- chapter 2 Solution of the inverse problem on the half-line -- chapter 3 Differential operators with a simple spectrum -- chapter 4 Solution of the inverse problem on a finite interval -- chapter 5 Inverse problems for the self-adjoint case -- chapter 6 Differential operators with singularities -- chapter 7 Differential operators with a "separate" spectrum -- chapter 8 Stability of the solution of the inverse problem -- chapter 9 Method of standard models. Information condition -- chapter 10 An inverse problem of elasticity theory -- chapter 11 Differential operators with locally integrable coefficients -- chapter 12 Discrete inverse problems. Applications to differential operators -- chapter 13 Inverse problems for integro-differential operators.
Analytical methods and special functions