Linear dynamics in reproducing kernel Hilbert spaces

Abstract

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, for all f ∈ H and w ∈ D. We analyze the special case of quasi-scalar 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.∂ 2n k ∂z n ∂w n (0, 0) = 0.

On the solutions of boundary value problems

“…Agud et al [4] have investigated the weighted p-regular kernels for reproducing kernel Hilbert spaces. Mundayadan et al [5] have studied on the linear dynamics in the reproducing kernel Hilbert spaces. Arqub et al [6] have constructed the modulation of reproducing kernel technique successfully.…”