Overview

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. This book presents an extensive overview of logarithmic integral operators with kernels depending on one or several complex parameters. Solvability of corresponding boundary value problems and determination of characteristic numbers are analyzed by considering these operators as operator-value functions of appropriate complex (spectral) parameters. Therefore, the method serves as a useful addition to classical approaches. Special attention is given to the analysis of finite-meromorphic operator-valued functions, and explicit formulas for some inverse operators and characteristic numbers are developed, as well as the perturbation technique for the approximate solution of logarithmic integral equations. All essential properties of the generalized single- and double-layer potentials with logarithmic kernels and Green's potentials are considered. Fundamentals of the theory of infinite-matrix summation operators and operator-valued functions are presented, including applications to the solution of logarithmic integral equations. Many boundary value problems for the two-dimensional Helmholtz equation are discussed and explicit formulas for Green's function of canonical domains with separated logarithmic singularities are presented.

Full Product Details

Author:   Yu V. Shestopalov ,  Yu G. Smirnov ,  E. V. Chernokozhin
Publisher:   Brill
Imprint:   VSP International Science Publishers
Dimensions:   Width: 17.80cm , Height: 1.30cm , Length: 25.40cm
Weight:   0.410kg
ISBN:  

9789067643221

ISBN 10:   906764322
Pages:   118
Publication Date:   24 February 2000
Recommended Age:   College Graduate Student
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Introduction 1. ELEMENTS OF THE THEORY OF INTEGRAL OPERATORS Integral operators with purely logarithmic kernel Integral operators in Hoelder spaces Logarithmic integral operators and Chebyshev polynomials Integral operators defined on a set of intervals Integral operators with fixed logarithmic singularities Elements of spectral theory Abstract pole pencils Logarithmic integral operators in Sobolev spaces Integral operators with kernels represented by series Methods of small parameter Approximate inversion Approximate semi-inversion 2. GENERALIZED POTENTIALS WITH LOGARITHMIC KERNELS Generalized potentials Green's potentials Examples for canonical domains Half plane Rectangle Circle Exterior of a circle Ring 3. SUMMATION OPERATORS Matrix representation Galerkin methods and basis of Chebyshev polynomials Summation operators in the spaces of sequences Matrix representation of logarithmic integral operators 4. BOUNDARY VALUE PROBLEMS Formulation of the problems Uniqueness and existence theorems Canonical problems: diffraction by strips and slots Diffraction by a slot Diffraction by a strip Diffraction by a screen with a rectangular slotted cavity Scattering by a circular slotted cylinder Eigenoscillations of open and closed slot resonators Closed rectangular slot resonator Open rectangular slot resonator Slotted resonator with circular cross section The integral and summation equations for the strip problems Summation equations in the problem on eigenfrequencies Bibliography

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