Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators
Functional Analysis
2024-12-30 v1
Abstract
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions within these spaces, and in particular, we provide an analog of the Paley-Wiener theorem in this setting. As an application, we consider Toeplitz operators with vertical symbols in these new spaces.
Keywords
Cite
@article{arxiv.2412.18954,
title = {Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators},
author = {Zhirayr Avetisyan and Alexey Karapetyants and Irina Smirnova},
journal= {arXiv preprint arXiv:2412.18954},
year = {2024}
}