No entire inner functions

TL;DR

This paper characterizes entire inner functions within a broad class of Reproducing Kernel Hilbert Spaces, demonstrating that only normalized monomials qualify as entire inner functions.

Contribution

It provides a complete classification of entire inner functions in these spaces, identifying normalized monomials as the only such functions.

Findings

Normalized monomials are the only entire inner functions.

The result applies to a large family of Reproducing Kernel Hilbert Spaces.

The study advances understanding of the structure of inner functions.

Abstract

We study generalized inner functions on a large family of Reproducing Kernel Hilbert Spaces. We show that the only inner functions that are entire are the normalized monomials.