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Simultaneous pairs of dual integral equations

Westmann, R. A. (1965) Simultaneous pairs of dual integral equations. SIAM Review, 7 (3). pp. 341-348. ISSN 0036-1445. https://resolver.caltech.edu/CaltechAUTHORS:20120921-103525337  Preview
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Abstract

A fruitful method of attack in the solution of mixed boundary value problems is the utilization of integral transform techniques. Satisfaction of the mixed boundary conditions then leads to consideration of one or more pairs of dual integral equations. Oftentimes the solution of these dual integral equations only follows from laborious and complex manipulations. An exception to this is the work of Copson  and Lowengrub, Sneddon  in which the general solution to the pair of dual integral equations (1a) ∫_(0)^(∞)ψ(ξ)J_(v)(ξr) dξ = f1(r), 1<r<∞, (1b) ∫_(0)^(∞)ψ(ξ)ξ^(2a)J_(v)(ξr) dξ=f2(r), 0<r<1, is obtained in a simple and straightforward manner. It is the purpose of this article to demonstrate that the solution techniques in ,  are equally applicable for the simultaneous pairs of dual integral equations ∫_(0)^(∞) [aψ1(ξ)+ψ2(ξ)]J(v+2)(ξr)dξ=f1(r), 1<r<∞, ∫_(0)^(∞) [bψ1(ξ)+ψ2(ξ)]ξ^(2a)J_(v+2)(ξr)dξ=f2(r), 0<r<1, ∫_(0)^(∞) [cψ1(ξ)+ψ2(ξ)]J(v+2)(ξr)dξ=f3(r), 1<r<∞, ∫_(0)^(∞) [ψ1(ξ)+ψ2(ξ)]ξ^(2a)J_(v)(ξr)dξ=f4(r), 0<r<1.

Item Type:Article
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http://dx.doi.org/10.1137/1007068DOIUNSPECIFIED
http://epubs.siam.org/doi/abs/10.1137/1007068PublisherUNSPECIFIED
Additional Information:© 1965 SIAM. Received by the editors November 19, 1963, and in revised form August 12, 1964.
Issue or Number:3
Record Number:CaltechAUTHORS:20120921-103525337
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120921-103525337
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34278
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:21 Sep 2012 21:25