The Weyl calculus with respect to the Gaussian measure and restricted Lp-Lq boundedness of the Ornstein-Uhlenbeck semigroup in complex time

DOI10.24033/bsmf.2771OpenAlexW2597187945WikidataQ128442480 ScholiaQ128442480MaRDI QIDQ5380611

Pierre Portal, J. M. A. M. van Neerven

Publication date: 5 June 2019

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.03602

zbMATH Keywords

canonical commutation relationOrnstein-Uhlenbeck operatorWeyl functional calculusMehler kernelrestricted \(L^p\)-\(L^q\)-boundednessrestricted Sobolev embeddingSchur estimate

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Functional calculus for linear operators (47A60) Stochastic calculus of variations and the Malliavin calculus (60H07) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Pseudodifferential operators (47G30)

Related Items (3)

Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices ⋮ A Weyl pseudodifferential calculus associated with exponential weights on \(\mathbb{R}^d\) ⋮ Optimal angle of the holomorphic functional calculus for the Ornstein-Uhlenbeck operator

Cites Work

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• The hypercontractive approach to exactly bounding an operator with complex Gaussian kernel
• Two-point inequalities, the Hermite semigroup, and the Gauss-Weierstrass semigroup
• On complex hypercontractivity
• Dimension dependent hypercontractivity for Gaussian kernels
• Tensor Algebras Over Hilbert Spaces. I
• Functional calculus for the Ornstein-Uhlenbeck operator

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