Direct and reverse log-Sobolev inequalities in $\mu$-deformed Segal-Bargmann analysis

Carlos Ernesto Angulo Aguila, Stephen Bruce Sontz

Both direct and reverse log-Sobolev inequalities, relating the Shannon entropy with a $\mu$-deformed energy, are shown to hold in a family of $\mu$-deformed Segal-Bargmann spaces. This…