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Convolutions for Berezin quantization and Berezin-Lieb inequalities
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Concepts and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, are identified as the appropriate setting for Berezin quantization and Berezin-Lieb inequalities. Based on this insight, we provide a rigorous approach to the 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 the Berezin quantization and Weyl quantization.
Title: Convolutions for Berezin quantization and Berezin-Lieb inequalities
Description:
Concepts and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, are identified as the appropriate setting for Berezin quantization and Berezin-Lieb inequalities.
Based on this insight, we provide a rigorous approach to the 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 the Berezin quantization and Weyl quantization.
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