Cowen-Douglas operators and analytic continuation
Functional Analysis
2025-08-12 v1 Complex Variables
Differential Geometry
Spectral Theory
Abstract
In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left inverse is a Cowen-Douglas operator. We investigate how the analytic continuations of functions from an invariant subspace of this Cowen-Douglas operator relate to the spectrum of its restriction to that subspace.
Cite
@article{arxiv.2505.05649,
title = {Cowen-Douglas operators and analytic continuation},
author = {Paweł Pietrzycki},
journal= {arXiv preprint arXiv:2505.05649},
year = {2025}
}
Comments
This is a very preliminary version