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
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.
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