General Optimal Polynomial Approximants, Stabilization, and Projections of Unity (Analysis in Theory and Applications, 2023)
In various Hilbert spaces of analytic functions on the unit disk, we characterize when a function has optimal polynomial approximants given by truncations ofa single power series or, equivalently, when the approximants stabilize. We also introduce a generalized notion of optimal approximant and use this to explicitly computeorthogonal projections of 1 onto certain shift invariant subspaces.