Logarithmic Integral Equations in Electromagnetics
VSP International Science Publishers (Verlag)
978-90-6764-322-1 (ISBN)
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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.
Introduction
1. ELEMENTS OF THE THEORY OF INTEGRAL OPERATORS
Integral operators with purely logarithmic kernel
Integral operators in Hölder 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
| Erscheint lt. Verlag | 1.2.2000 |
|---|---|
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 395 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik | |
| ISBN-10 | 90-6764-322-X / 906764322X |
| ISBN-13 | 978-90-6764-322-1 / 9789067643221 |
| Zustand | Neuware |
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