International Journal of Mathematics and Mathematical Sciences 
Volume 27 (2001), Issue 4, Pages 221-228
doi:10.1155/S0161171201010584

Convolution algebras arising from Sturm-Liouville transforms and applications

Jason P. Huffman1 and Henry E. Heatherly2

 1Department of Mathematics, Computing, and Information Sciences, Jacksonville State University, Jacksonville 36265, AL, USA
2Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504, LA, USA
Received 14 July 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.