Measures not charging semipolars and equations of Schrödinger type
type: Item
instance of: scholarly article
title: Measures not charging semipolars and equations of Schrödinger type
zbMATH Open document ID: 0816.60077
DOI: 10.1007/BF01048968
published in: Potential Analysis
publication date: 1995-07-06T00:00:00Z
review text: Let \(X\) be a (Borel) right Markov process with distinguished excessive measure \(m\). The author establishes a bijection between a certain class of multiplicative functionals of \(X\) and the class of (equivalence classes of) measures on the state space of \(X\) charging no \(m\)-semipolar set. (Two such measures are equivalent provided they put the same mass on each finely open set.) The author then uses this bijection to study questions of existence and uniqueness for the Schrödinger-type equation \((q-L)u+ u\mu= f\), where \(q> 0\), \(L\) is the infinitesimal generator of \(X\), and \(f\) is a suitable function. This work generalizes an earlier study of \textit{J. Baxter}, \textit{G. Dal Maso} and \textit{U. Mosco} [Trans. Am. Math. Soc. 303, 1-38 (1987; Zbl 0627.60071)], and also extends work of \textit{K.-T. Sturm} [Forum Math. 4, No. 3, 257-297 (1992; Zbl 0745.60080)] and \textit{K. Kuwae} [ibid., to appear].
Mathematics Subject Classification ID: 60J40
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J57
zbMATH DE Number: 723922
zbMATH Keywords: Markov processes
zbMATH Keywords: multiplicative functionals
zbMATH Keywords: semipolar sets
zbMATH Keywords: Schrödinger equations
author: R. K. Getoor
reviewed by: Patrick J. Fitzsimmons
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 723922