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Optimal Holomorphic Hypercontractivity for CAR Algebras

Ilona Królak (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We present a new proof of Janson’s strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (canonical anticommutation relations) algebras. In the one generator case we calculate optimal bounds for t such that U t is a contraction as a map L ( ) L p ( ) for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.

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