Quantum Harmonic Analysis for Polyanalytic Fock Spaces

verfasst von

Robert Fulsche, Raffael Hagger

Abstract

We develop the quantum harmonic analysis framework in the reducible setting and apply our findings to polyanalytic Fock spaces. In particular, we explain some phenomena observed in recent work by the second author and answer a few related open questions. For instance, we show that there exists a symbol such that the corresponding Toeplitz operator is unitary on the analytic Fock space but vanishes completely on one of the true polyanalytic Fock spaces. This follows directly from an explicit characterization of the kernel of the Toeplitz quantization, which we derive using quantum harmonic analysis. Moreover, we show that the Berezin transform is injective on the set of of Toeplitz operators. Finally, we provide several characterizations of the C₁-algebra in terms of integral kernel estimates and essential commutants.

Organisationseinheit(en)

Institut für Analysis

Externe Organisation(en)

Christian-Albrechts-Universität zu Kiel (CAU)

Typ

Artikel

Journal

Journal of Fourier Analysis and Applications

Band

30

ISSN

1069-5869

Publikationsdatum

01.11.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Allgemeine Mathematik, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1007/s00041-024-10124-9 (Zugang: Offen)