Analysis IV
Linear and Boundary Integral Equations
Editors: Maz'ya, V.G., Nikol'skii, S.M. (Eds.)
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A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x)  Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with afinite measure v, 2 is a complex parameter, and a, k, f are given (complexvalued) functions, which are referred to as the coefficient, the kernel, and the free term (or the righthand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vectorvalued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integral equations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Analysis IV
 Book Subtitle
 Linear and Boundary Integral Equations
 Editors

 V.G. Maz'ya
 S.M. Nikol'skii
 Translated by
 Prössdorf, S., Böttcher, A.
 Series Title
 Encyclopaedia of Mathematical Sciences
 Series Volume
 27
 Copyright
 1991
 Publisher
 SpringerVerlag Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 eBook ISBN
 9783642581755
 DOI
 10.1007/9783642581755
 Softcover ISBN
 9783642634918
 Series ISSN
 09380396
 Edition Number
 1
 Number of Pages
 VII, 236
 Additional Information
 Original Russian edition published by Publisher VINITI, Moscow, 1988
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