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Affine Quantum Harmonic Analysis (2102.13006v1)
Published 25 Feb 2021 in math.FA, math-ph, and math.MP
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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