On Complex Hypercontractivity

  title={On Complex Hypercontractivity},
  author={Svante Janson},
  journal={Journal of Functional Analysis},
  • S. Janson
  • Published 1 December 1997
  • Mathematics
  • Journal of Functional Analysis
Abstract We give a new proof of a hypercontractivity theorem for the Mehler transform with a complex parameter, earlier proved by Weissler (1979, J. Funct. Anal. 32 , 102–121) and Epperson (1989, J. Funct. Anal. 87 , 1–30). The proof uses stochastic integrals and Ito calculus. The method also yields new proofs of some related results. 

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