Sharp bounds for the first eigenvalue of symmetric Markov processes and their applications
type: Item
instance of: scholarly article
title: Sharp bounds for the first eigenvalue of symmetric Markov processes and their applications
zbMATH Open document ID: 1263.60069
author: Jian Wang
publication date: 2013-01-02T00:00:00Z
review text: Let \(X\) be a reversible Markov process on a locally compact, separable metric space, with symmetric measure \(\mu \). Let \(L\) denote its infinitesimal operator on \(L^2(\mu )\). Introducing a transform of this operator, \(L_ {\rho } f := \frac{L(\rho f)}{\rho } - \frac{L(\rho )}{\rho } f\) (for a strictly positive function \(\rho \)), the author gives lower and upper bounds for the first eigenvalue of \(L\). This result covers the lower bound found by \textit{M. Chen} [Acta Math. Sin., Engl. Ser. 16, No. 3, 361--368 (2000; Zbl 0963.60078)]. Further, the author uses his result to obtain approximation procedures for the first eigenvalue of birth-death processes with killing and qualitatively sharp upper and lower bounds for the first eigenvalue of elliptic operators with killing on half line.
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 6121162
zbMATH Keywords: first eigenvalue
zbMATH Keywords: symmetric Markov process
zbMATH Keywords: birth-death process with killing
zbMATH Keywords: elliptic operators with killing
reviewed by: Liliana Popa
MaRDI profile type: Publication
full work available at URL: s10114-012-1023-1
OpenAlex ID: W1982209243
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DOI: 10.1007/S10114-012-1023-1
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6121162