HYPERCYCLICITY OF AFFINE COMPOSITION OPERATORS ON ALGEBRAS OF SYMMETRIC ANALYTIC FUNCTIONS - Zoriana Novosad (Institute of Mathematics of the National Academy of Sciences of Ukraine., 2024)
Abstract. The paper is devoted to studying the dynamics of affine composition operators on the Fr´echet algebras of symmetric analytic functions on \ell p.We introduced a class of affine composition operators preserving the symmetry of functions and found necessary and sufficient conditions of hypercyclicity of such operators. Some applications for dynamics of composition operators on the space of entire functions of several complex variables, H(Cn) are proposed. In particular, we found some conditions of hypercyclicity for a class of polynomial composition operators on H(Cn).
Methods of Functional Analysis and Topology Vol. 30 (2024), no. 1-2,
Keywords: Hypercyclic operators; functional spaces; topological automorphisms; symmetric functions