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On two reverse inequalities in the Segal-Bargmann space. (English) Zbl 0968.46062

Summary: We review here two reverse inequalities in the Segal-Bargmann space: A reverse hypercontractivity estimate due to Carlen and a reverse log-Sobolev inequality due to the second author.

MSC:

46N50 Applications of functional analysis in quantum physics
47D03 Groups and semigroups of linear operators
81S99 General quantum mechanics and problems of quantization
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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