Linchuk Y. Some classes of the operators which act in spaces of analytical functions and related with correlations of commutation

In thesis the solutions of some operator equations which contain operators of the generalized shift, operators of the composition, operators of the generalized derivations and operators of the generalized integrations are investigated. Images of linear continuous operators which commute with the operators connected with usual and generalized shifts and acting in spaces of polynomials and spaces of functions, which are analytical in arbitrary domains, are received. In general case concerning domains, conditions of the equivalence of the operators of the generalized shift, which generated by Pomme operator, are studied . The commutant of the composition operator in space of functions which are analytic in the unit disk, which generated by the arbitrary fixed automorphism of the unit disk is described. The solutions of some operator equations which are connected with operators of the generalized derivation and of the generalized integration in class of linear continuous operators which acting in spaces ofanalytical in arbitrary domains functions are investigated.