Symmetric Lévy type operator
type: Item
instance of: scholarly article
title: Symmetric Lévy type operator
zbMATH Open document ID: 1181.60116
author: Jian Wang
publication date: 2009-11-11T00:00:00Z
review text: The paper presents some sufficient conditions for the existence of a symmetric measure for a Lévy type operator: \[ \begin{multlined} L f (x) = \sum _ {i, j = 1}^ {d} a_ {i j} (x) \partial _ {i j} f(x) + \sum _ {i=1}^ {d} b_ {i} (x) \partial _ {i} f(x) + \int _ {\mathbb{R}^ {d} \setminus \{ 0 \}}\\ \left ( f(x+z) - f(x) - {\mathbf 1}_ {|z| \leq 1} \sum _ {i=1}^ {d} z_ {i} \partial _ {i} f(x) \right ) \nu (x, d z)\end{multlined} \] where: \((a_ {i j}(x))\) is non-negative definite matrix of functions of class \({\mathcal C}^ {2}\); \((b_ {i}(x))\) a vector of measurable functions and \(\nu (x, d z)\) is a Lévy jump measure kernel.
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 5629481
zbMATH Keywords: Lévy type generator
zbMATH Keywords: symmetric measure
MaRDI profile type: Publication
full work available at URL: s10114-008-7154-8
OpenAlex ID: W2099402428
cites work: Invariant measures and symmetry property of Lévy type operators
cites work: Estimation of spectral gap for elliptic operators
cites work: Dirichlet forms and symmetric Markov processes
cites work: Q4650356
cites work: On the Feller property of Dirichlet forms generated by pseudo differential operators
DOI: 10.1007/S10114-008-7154-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629481