International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 27 |Article ID 724684 | https://doi.org/10.1155/S0161171201010584

Jason P. Huffman, Henry E. Heatherly, "Convolution algebras arising from Sturm-Liouville transforms and applications", International Journal of Mathematics and Mathematical Sciences, vol. 27, Article ID 724684, 8 pages, 2001. https://doi.org/10.1155/S0161171201010584

Convolution algebras arising from Sturm-Liouville transforms and applications

Received14 Jul 2000

Abstract

A regular Sturm-Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this fashion from a regular Sturm-Liouville problem. We give applications of these convolution algebras for solving certain differential and integral equations, and we outline an operational calculus for classes of such equations.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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