On Shannon entropies in μ-deformed Segal-Bargmann analysis

We consider a ${\mu}$-deformation of the Segal-Bargmann transform, which is aunitary map from a ${\mu}$-deformed quantum configuration space onto a${\mu}$-deformed quantum phase space (the ${\mu}$-deformed Segal-Bargmannspace). Both of these Hilbert spaces have canonical orthonormal bases. Weobtain explicit formulas for the Shannon entropy of some of the elements ofthese bases. We also consider two reverse log-Sobolev inequalities in the${\mu}$-deformed Segal-Bargmann space, which have been proved in a previouswork, and show that a certain known coefficient in them is the best possible.