© Hindawi Publishing Corp. CONVOLUTION ALGEBRAS ARISING FROM STURM-LIOUVILLE TRANSFORMS AND APPLICATIONS

Abstract. A regular Sturm-Liouville eigenvalue problem gives rise to a related linear inte-gral 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. 2000 Mathematics Subject Classification. 16S60, 44A40. 1. Introduction. Convolutio