Finite speed of propagation and off-diagonal bounds for Ornstein–Uhlenbeck operators in infinite dimensions
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- 作者：Jan van Neerven ; Pierre Portal
- 关键词：Ornstein–Uhlenbeck operator ; Hodge–Dirac operator ; \(C_0\) ; group ; Finite speed of propagation ; Heat kernel bounds ; Davies–Gaffney estimates
- 刊名：Annali di Matematica Pura ed Applicata
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：195
- 期：6
- 页码：1889-1915
- 全文大小：625 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1618-1891
- 卷排序：195
文摘
We study the Hodge–Dirac operators \({\mathscr {D}}\) associated with a class of non-symmetric Ornstein–Uhlenbeck operators \({\mathscr {L}}\) in infinite dimensions. For \(p\in (1,\infty )\) we prove that \(i{\mathscr {D}}\) generates a \(C_0\)-group in \(L^p\) with respect to the invariant measure if and only if \(p=2\) and \({\mathscr {L}}\) is self-adjoint. An explicit representation of this \(C_0\)-group in \(L^2\) is given, and we prove that it has finite speed of propagation. Furthermore, we prove \(L^2\) off-diagonal estimates for various operators associated with \({\mathscr {L}}\), both in the self-adjoint and the non-self-adjoint case.