Analogues of Finite Blaschke Products as Inner Functions

Abstract

We give a generalization of the notion of finite Blaschke products from the perspective of generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these functions relate to the so-called Shapiro--Shields functions and shift-invariant subspaces generated by polynomials. Applying our results, we show that the only entire inner functions on weighted Hardy spaces over the unit disk are multiples of monomials, extending recent work of Cobos and Seco.

Final version

References in corpus (4)

• Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants
• Remarks on Inner Functions and Optimal Approximants
• Inner functions and operator theory
• General Optimal Polynomial Approximants, Stabilization, and Projections of Unity