Analogues of Finite Blaschke Products as Inner Functions
Functional Analysis
2022-06-07 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.2105.01766,
title = {Analogues of Finite Blaschke Products as Inner Functions},
author = {Christopher Felder and Trieu Le},
journal= {arXiv preprint arXiv:2105.01766},
year = {2022}
}
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Final version