  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.
