Inverse Spectral Problems for Linear Differential Operators and Their Applications

1. Auflage 2000
ISBN: 978-90-5699-189-0
Verlag: CRC Press

Buch, Englisch, 272 Seiten, Format (B × H): 175 mm x 253 mm, Gewicht: 735 g

Reihe: Analytical Methods and Special Functions

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.

Autoren/Hrsg.

Yurko, V. A.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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

Über Autor(innen)

Yurko, V A