Bitangential direct and inverse problems for systems of integral and differential equations / Damir Z. Arov, Harry Dym.

Format:

Book

Author/Creator:

Arov, Damir Z., author.

Dym, Harry, 1934- author.

Series:

Encyclopedia of mathematics and its applications ; v. 145.

Encyclopedia of mathematics and its applications ; volume 145

Language:

English

Subjects (All):

Inverse problems (Differential equations).

Integral equations.

Physical Description:

1 online resource (xiv, 472 pages) : digital, PDF file(s).

Other Title:

Bitangential Direct & Inverse Problems for Systems of Integral & Differential Equations

Place of Publication:

Cambridge : Cambridge University Press, 2012.

Language Note:

English

Summary:

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.

Contents:

Introduction

Canonical systems and related differential equations

Matrix-valued functions in the Nevanlinna class

Interpolation problems, resolvent matrices and de Branges spaces

Chains that are matrizants and chains of associated pairs

The bitangential direct input scattering problems

Bitangential direct input impedance and spectral problems

Inverse monodromy problems

Bitangential Krein extension problems

Bitangential inverse input scattering problems

Bitangential inverse input impedance and spectral problems

Direct and inverse problems for Dirac-Krein systems.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88757-2

1-139-55586-3

1-139-55461-1

1-139-55215-5

1-139-54965-0

1-139-09351-7

1-283-63831-2

1-139-55090-X

OCLC:

813396550