CONDITIONS OF INVERTIBILITY FOR FUNCTIONAL OPERATORS WITH SHIFT IN WEIGHTED HO¨ LDER SPACES

Abstract

We consider functional operators with shift in weighted H¨older spaces. The main result of this work is the proof of the conditions of invertibility for these operators. We also indicate the forms of the inverse operator. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.