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

Analysis

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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 - 28 Oct 2015

Keywords

Ornstein–Uhlenbeck operator
Hodge–Dirac operator
C0-group
Finite speed of propagation
Heat kernel bounds
Davies–Gaffney estimates

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10.1007/s10231-015-0541-8

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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 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.",

keywords = "Ornstein–Uhlenbeck operator, Hodge–Dirac operator, C0-group, Finite speed of propagation, Heat kernel bounds, Davies–Gaffney estimates",

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

AU - van Neerven, Jan

AU - Portal, Pierre

PY - 2015/10/28

Y1 - 2015/10/28

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 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.

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 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.

KW - Ornstein–Uhlenbeck operator

KW - Hodge–Dirac operator

KW - C0-group

KW - Finite speed of propagation

KW - Heat kernel bounds

KW - Davies–Gaffney estimates

U2 - 10.1007/s10231-015-0541-8

DO - 10.1007/s10231-015-0541-8

M3 - Article

SN - 0373-3114

VL - 195

SP - 1889

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

Abstract

Keywords

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