Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Function-theoretic solution to a class of dual integral equations and an application to diffraction theory

Authors: Robert A. Schmeltzer and Myrna Lewin
Journal: Quart. Appl. Math. 21 (1964), 269-283
DOI: https://doi.org/10.1090/qam/155162
MathSciNet review: 155162
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Abstract: Dual integral equations of the type

$\displaystyle \int_0^\infty {{u^\lambda }f\left( u \right){J_\mu }\left( {ru} \... ...eft( u \right){J_v}\left( {ru} \right)du = h\left( r \right),} 1 < r < \infty ,$

where $ g\left( r \right)$, $ h\left( r \right)$ are prescribed functions and $ f\left( u \right)$ is to be found, are solved exactly by the application of function-theoretic methods. As an example, a closed-form solution is obtained for the diffraction of an electromagnetic wave by a plane slit.

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DOI: https://doi.org/10.1090/qam/155162
Article copyright: © Copyright 1964 American Mathematical Society

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