Convolution algebras arising from Sturm-Liouville transforms and applications - Jason P. Huffman; Henry E. Heatherly (International Journal of Mathematics and Mathematical Sciences)
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.