Affine Quantum Harmonic Analysis
Eirik Berge, Stine M. Berge, Franz Luef, and Eirik Skrettingland
TL;DR
This paper introduces a quantum harmonic analysis framework for the affine group, unifying various existing concepts like affine localization and affine quadratic time-frequency representations, and extends key results to operators.
Contribution
It develops a novel quantum harmonic analysis framework for the affine group, including a new notion of admissibility for operators and extending classical results to the operator setting.
Findings
Unified framework for affine localization and quantization
Extended admissibility concepts to operators
Connected operator convolutions with affine Weyl quantization
Abstract
We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integral quantizations, and affine quadratic time-frequency representations. In the process, we develop a notion of admissibility for operators and extend well known results to the operator setting. A major theme of the paper is the interaction between operator convolutions, affine Weyl quantization, and admissibility.
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