Approximation in Weighted Analytic Besov Spaces and in Generalized Fock Spaces

We study weighted analytic Besov spaces in the unit disk, and prove that the analytic polynomials are dense in weighted analytic Besov spaces if the non-radial super-biharmonic weight function satisfies certain smoothness and growth condition. We then study sufficient conditions on weight functions to ensure the norm approximation of a given function in a generalized weighted Fock space by its dilated functions.