Convolutions for Berezin quantization and Berezin-Lieb inequalities

Abstract

Notions and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, is identified as the appropriate setting for Berezin quantization and Berezin-Lieb inequalities. Based on this insight we provide a rigorous approach to generalized phase-space representation introduced by Klauder-Skagerstam and their variants of Berezin-Lieb inequalities in this setting. Hence our presentation of the results of Klauder-Skagerstam gives a more conceptual framework, which yields as a byproduct an interesting perspective on the connection between Berezin quantization and Weyl quantization.

References in corpus (6)

• Schwartz operators
• A unified approach to infinite dimensional integration
• Positive operator valued measures covariant with respect to an irreducible representation
• Characterization of informational completeness for covariant phase space observables
• Generalized Phase Space Representation of Operators
• The spectrogram expansion of Wigner functions

Cited by in corpus (2)

• Quantum harmonic analysis on locally compact groups
• Measure-operator convolutions and applications to mixed-state Gabor multipliers