Classes of convolution type operators on unions of bounded intervals

Abstract

An invertibility theory for classes of convolution type operators on a union of bounded intervals whose kernels have Fourier transforms which are related to solutions of corona problems is established and the corresponding formulas for the inverse operators are given. A generalization of the portuguese transformation for matrix functions is obtained and is used to establish the invertibility theory for one of the above mentioned classes of operators. The same transformation allows, also, to establish the equivalence between convolution type operators on an union of disjoint intervals and convolution type operators on a bounded interval.