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Yu.V. Shestopalov, Yu.G. Smirnov and E.V. Chernokozhin
This book presents an extensive overview of logarithmic integraloperators with kernels depending on one or several complexparameters. Solvability of corresponding boundary value problems anddetermination of characteristic numbers are analyzed by consideringthese operators as operator-value functions of appropriate complex(spectral) parameters. Therefore, the method serves as a usefuladdition to classical approaches.
Special attention is given to the analysis of finite-meromorphicoperator-valued functions, and explicit formulas for some inverseoperators and characteristic numbers are developed, as well as theperturbation technique for the approximate solution of logarithmicintegral equations. All essential properties of the generalizedsingle- and double-layer potentials with logarithmic kernels andGreen's potentials are considered. Fundamentals of the theory ofinfinite-matrix summation operators and operator-valued functions arepresented, including applications to the solution of logarithmicintegral equations. Many boundary value problems for thetwo-dimensional Helmholtz equation are discussed and explicitformulas for Green's function of canonical domains with separatedlogarithmic singularities are presented.
This book, presenting all necessary references to the spectraltheory, will serve as an efficient instrument for the analysis oflogarithmic integral equations and will be of value and interest toresearchers in the field of mathematical physics, theoreticalelectromagnetics, integral equations and spectral theory of operators.
2000; xii+118 pages
ISBN 90-6764-322-X
Price (all prices are subject to change without notice): EUR 92/US$ 132
VSPPostal address: P.O. Box 9000, 2300 PA Leiden, The Netherlands