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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. doi:10.1137/1007068.

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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 [1] and Lowengrub, Sneddon [2] 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 [1], [2] 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.

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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
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34278
Deposited On:21 Sep 2012 21:25
Last Modified:09 Nov 2021 23:07

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