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

Jan van Neerven, Pierre Portal

Research output: Contribution to journalArticleScientificpeer-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 languageEnglish
Pages (from-to)1889-1915
Number of pages27
JournalAnnali di Matematica Pura ed Applicata
Volume195
Issue number6
DOIs
Publication statusPublished - 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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