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arXiv · 2412.18954

Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators

Zhirayr Avetisyan·Alexey Karapetyants·Irina Smirnova
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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.

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Zhirayr Avetisyan, Alexey Karapetyants, Irina Smirnova. 2024-12-25. Mixed Fourier norm spaces of analytic functions on the upper half-plane and Toeplitz operators. https://arxiv.org/abs/2412.18954

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