Estimates for elements of inverse matrices for a class of operators with matrices of special structure (Q1810155)

The author obtains specific (not asymptotic) estimates for the elements of inverse matrices of bounded linear operators acting in infinite-dimensional complex Banach spaces. The matrices of these operators have a special structure and are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given functions on elements of a special nondiagonal partition of the index set. The estimates are derived from an analysis of Fourier series of strongly continuous periodic functions.