Polynomial approach to cyclicity for weighted ¿pA

In previous works, an approach to the study of cyclic functions in reproducing kernel Hilbert spaces has been presented, based on the study of so called optimal polynomial approximants. In the present article, we extend such approach to the (non-Hilbert) case of spaces of analytic functions whose Taylor coefficients are in ℓp(omega), for some weight omega. When omega={(k+1)alfa}k∈N, for a fixed alfa∈R, we derive a characterization of the cyclicity of polynomial functions and, when 1 < p < ∞, we obtain sharp rates of convergence of the optimal norms.

Polynomial approach to cyclicity for weighted ¿pA Articles