Linear dynamics in reproducing kernel Hilbert spaces

Complementing earlier results on dynamics of unilateral weighted shifts, we obtain a sufficient (but not necessary, with supporting examples) condition for hypercyclicity, mixing and chaos for M-z*, the adjoint of M-z, on vector-valued analytic reproducing kernel Hilbert spaces H in terms of the derivatives of kernel functions on the open unit disc D in C. Here M-z denotes the multiplication operator by the coordinate function z, that is (M(z)f)(w) = wf (w), for all f is an element of H and w is an element of D. We analyze the special case of quasiscalar reproducing kernel Hilbert spaces. We also present a complete characterization of hypercyclicity of M-z* on tridiagonal reproducing kernel Hilbert spaces and some special classes of vector-valued analytic reproducing kernel Hilbert spaces. (C) 2019 Elsevier Masson SAS. All rights reserved.