Equations of Mathematical Diffraction TheoryCRC Press, 29 сент. 2004 г. - Всего страниц: 312 Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case. Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications. |
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Equations of Mathematical Diffraction Theory Mezhlum A. Sumbatyan,Antonio Scalia Недоступно для просмотра - 2004 |
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Abramowitz and Stegun acoustically hard algebraic system algorithm amplitude analytic angle applied approximation arbitrary boundary conditions boundary value problem calculation classical coefficients considered convergence convex convex hull coordinate system differential diffraction diffraction problem diffraction theory Dirichlet domain eigenvalues elastic estimate example finite formula Fourier transform Fredholm Fredholm integral equation frequency Green's formula Green's function half-plane Helmholtz equation Helpful remarks hence high-frequency Hilbert space homogeneous ill-posed incident wave infinity integral equation integral operator integrand inverse problem iterative kernel layer leading asymptotic term linear method nonconvex obstacle obtained operator equation oscillating parameter plane poles proved radiation condition reconstruction reflection representation right-hand side scalar scattered singular stationary point theorem unique unknown function vector wave field wave number zero αξ дпу др ду
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Стр. xii - Professor Slaught was a Fellow in Mathematics at the University of Chicago from 1892 to 1894, and was one of the first group of graduate students who received the Ph.D. degree in Mathematics from the University. From 1894 on he has been a member of the staff of the Department of Mathematics. He was a central figure in the founding of the Mathematical Association of America, and has been for many years managing editor of its official journal, the American Mathematical Monthly.