Ornstein–Uhlenbeck semigroups in infinite dimension-Reference-Cited by-同舟云学术

Ornstein–Uhlenbeck semigroups in infinite dimension

Published:2020-10-19 Issue:2185 Volume:378 Page:20190620
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Lunardi A.¹^ORCID,Pallara D.²

Affiliation:

1. Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy

2. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, and INFN, Sezione di Lecce. POB 193, 73100 Lecce, Italy

Abstract

This is a survey paper about Ornstein–Uhlenbeck semigroups in infinite dimension and their generators. We start from the classical Ornstein–Uhlenbeck semigroup on Wiener spaces and then discuss the general case in Hilbert spaces. Finally, we present some results for Ornstein–Uhlenbeck semigroups on Banach spaces. This article is part of the theme issue ‘Semigroup applications everywhere’.

Funder

Ministero dell'Istruzione, dell'Università e della Ricerca

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2019.0620

Reference43 articles.

1. Ornstein–Uhlenbeck operators and semigroups

2. Second Order Partial Differential Equations in Hilbert Spaces

3. Probability Distributions on Banach Spaces

4. A Hille-Yosida theorem for weakly continuous semigroups

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