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

Journal article (2015)

Authors

J.M.A.M. van Neerven Analysis - EEMCS
Pierre Portal Université de Lille, Australian National University
Research Group
Analysis (EEMCS) (TU Delft)
Hodge–Dirac operator Ornstein–Uhlenbeck operator C0-group Finite speed of propagation Heat kernel bounds Davies–Gaffney estimates
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Published Date

28-10-2015

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.