Algebraic results on rngs of singular functions

Abstract

We consider a Mikusinski-type convolution algebra C-alpha , including functions with power-type singularities at the origin as well as all functions continuous on [ 0 , infinity]. Algebraic properties of this space are derived, including its ideal structure, filtered and graded structure, and Jacobson radical. Applications to operators of fractional calculus and the associated integro-differential equations are discussed.