A WEIGHTED WIENER'S LEMMA FOR INTEGRAL OPERATORS WITH SCHUR-TYPE OR ESSENTIAL-SUPREMUM KERNEL DECAY CONDITIONS

In communication theory, one may encounter integral operators whose kernels' off-diagonal decay is strictly weaker than exponential. In this paper it is shown that if such an operator is invertible, the kernel of the inverse operator exhibits the same type of decay, extending the Banach *-algebraic techniques of Grochenig and Leinert in [7] to the setting of integral operators on the space of square-integrable functions. En route, symmetry of the algebras under consideration is established.