On the Ornstein-Uhlenbeck operator in spaces of continuous functions
type: Item
instance of: scholarly article
title: On the Ornstein-Uhlenbeck operator in spaces of continuous functions
zbMATH Open document ID: 0846.47004
author: Guiseppe Da Prato
author: Alessandra Lunardi
published in: Journal of Functional Analysis
publication date: 1996-03-20T00:00:00Z
review text: The authors study the realization of the Ornstein-Uhlenbeck operator \({\mathcal A}\) in the space of the uniform continuous and bounded functions in \(\mathbb{R}^n\). They prove that it generates a semigroup which is neither strongly continuous nor analytic, but enjoys nice smoothing properties. Such properties are used to prove a Schauder-type theorem for the elliptic equation \(\lambda u- {\mathcal A} u=f\).
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 847460
zbMATH Keywords: realization of the Ornstein-Uhlenbeck operator
zbMATH Keywords: space of the uniform continuous and bounded functions
zbMATH Keywords: semigroup which is neither strongly continuous nor analytic
zbMATH Keywords: smoothing properties
zbMATH Keywords: Schauder-type theorem
zbMATH Keywords: elliptic equation
MaRDI profile type: Publication
full work available at URL: jfan.1995.1084
OpenAlex ID: W2004930958
DOI: 10.1006/JFAN.1995.1084
description: scientific article; zbMATH DE number 847460