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

Details Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis

2007-07-21

arxiv.org/abs/0707.3227v1

Physics

Mathematical Physics

Accepted for publication in Infinite Dimensional Analysis, Quantum Probability and Related Topics

Scientific paper

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 shows that the $\mu$-deformed energy of a state is finite if and only if its Shannon entropy is finite. The direct inequality is a new result, while the reverse inequality has already been shown by the authors but using different methods. Next the $\mu$-deformed energy of a state is shown to be finite if and only if its Dirichlet form energy is finite. This leads to both direct and reverse log-Sobolev inequalities that relate the Shannon entropy with the Dirichlet energy. We obtain that the Dirichlet energy of a state is finite if and only if its Shannon entropy is finite. The main method used here is based on a study of the reproducing kernel function of these spaces and the associated integral kernel transform.

Affiliated with

Also associated with

No associations

Rating

Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-433900