Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations: 145 (Encyclopedia of Mathematics and its Applications, Series Number 145) - Hardcover

Arov, Damir Z.; Dym, Harry

Hardcover

ISBN 10: 1107018870 ISBN 13: 9781107018877

Publisher: Cambridge University Press, 2012

Synopsis

This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.

About this title

About the Authors

Damir Z. Arov is Professor in the Division of Applied Mathematics and Informatics at the South-Ukrainian Pedagogical University, Odessa.

Harry Dym is Professor Emeritus in the Department of Mathematics at the Weizmann Institute of Science, Rehovot, Israel.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2012
• Language: English
• ISBN 10: 1107018870
• ISBN 13: 9781107018877
• Binding: Hardcover
• Edition number: 1
• Number of pages: 488