Finite speed of propagation and off-diagonal bounds for Ornstein–Uhlenbeck operators in infinite dimensions

Jan van Neerven; Pierre Portal

doi:10.1007/s10231-015-0541-8

Finite speed of propagation and off-diagonal bounds for Ornstein–Uhlenbeck operators in infinite dimensions

Jan van Neerven, Pierre Portal^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study the Hodge–Dirac operators D associated with a class of non-symmetric Ornstein–Uhlenbeck operators L in infinite dimensions. For p∈ (1 , ∞) we prove that iD generates a C₀-group in L^p with respect to the invariant measure if and only if p= 2 and L is self-adjoint. An explicit representation of this C₀-group in L² is given, and we prove that it has finite speed of propagation. Furthermore, we prove L² off-diagonal estimates for various operators associated with L, both in the self-adjoint and the non-self-adjoint case.

Original language	English
Pages (from-to)	1889-1915
Number of pages	27
Journal	Annali di Matematica Pura ed Applicata
Volume	195
Issue number	6
DOIs	https://doi.org/10.1007/s10231-015-0541-8
Publication status	Published - 1 Dec 2016

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title = "Finite speed of propagation and off-diagonal bounds for Ornstein–Uhlenbeck operators in infinite dimensions",

abstract = "We study the Hodge–Dirac operators D associated with a class of non-symmetric Ornstein–Uhlenbeck operators L in infinite dimensions. For p∈ (1 , ∞) we prove that iD generates a C0-group in Lp with respect to the invariant measure if and only if p= 2 and L is self-adjoint. An explicit representation of this C0-group in L2 is given, and we prove that it has finite speed of propagation. Furthermore, we prove L2 off-diagonal estimates for various operators associated with L, both in the self-adjoint and the non-self-adjoint case.",

keywords = "C-group, Davies–Gaffney estimates, Finite speed of propagation, Heat kernel bounds, Hodge–Dirac operator, Ornstein–Uhlenbeck operator",

author = "{van Neerven}, Jan and Pierre Portal",

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T1 - Finite speed of propagation and off-diagonal bounds for Ornstein–Uhlenbeck operators in infinite dimensions

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AU - Portal, Pierre

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N2 - We study the Hodge–Dirac operators D associated with a class of non-symmetric Ornstein–Uhlenbeck operators L in infinite dimensions. For p∈ (1 , ∞) we prove that iD generates a C0-group in Lp with respect to the invariant measure if and only if p= 2 and L is self-adjoint. An explicit representation of this C0-group in L2 is given, and we prove that it has finite speed of propagation. Furthermore, we prove L2 off-diagonal estimates for various operators associated with L, both in the self-adjoint and the non-self-adjoint case.

AB - We study the Hodge–Dirac operators D associated with a class of non-symmetric Ornstein–Uhlenbeck operators L in infinite dimensions. For p∈ (1 , ∞) we prove that iD generates a C0-group in Lp with respect to the invariant measure if and only if p= 2 and L is self-adjoint. An explicit representation of this C0-group in L2 is given, and we prove that it has finite speed of propagation. Furthermore, we prove L2 off-diagonal estimates for various operators associated with L, both in the self-adjoint and the non-self-adjoint case.

KW - C-group

KW - Davies–Gaffney estimates

KW - Finite speed of propagation

KW - Heat kernel bounds

KW - Hodge–Dirac operator

KW - Ornstein–Uhlenbeck operator

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M3 - Article

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EP - 1915

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 6

ER -

Finite speed of propagation and off-diagonal bounds for Ornstein–Uhlenbeck operators in infinite dimensions

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