Electronic International Standard Serial Number (EISSN)
1565-8538
abstract
For functions f in Dirichlet-type spaces Dalfa, we study how to determine constructively optimal polynomials p n that minimize ∥pf−1∥alfa among all polynomials p of degree at most n. We then obtain sharp estimates for the rate of decay of ∥pnf−1∥alfa as n approaches ∞, for certain classes of functions f. Finally, inspired by the Brown-Shields conjecture, we prove that certain logarithmic conditions on f imply cyclicity, and we study some computational phenomena pertaining to the zeros of optimal polynomials.
Classification
subjects
Mathematics
keywords
bergman space; optimal norm; open unit disk; dirichlet space; closed disk