General Optimal Polynomial Approximants, Stabilization, and Projections of Unity

Abstract

For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal approximant and use this to explicitly compute orthogonal projections of 1 onto certain shift invariant subspaces.

16 pages; To appear in Analysis in Theory and Applications

References in corpus (2)

• Cyclicity in Dirichlet-type spaces and extremal polynomials
• Remarks on Inner Functions and Optimal Approximants

Cited by in corpus (1)

• Analogues of Finite Blaschke Products as Inner Functions