On combinatorics of Schrödinger perturbations
type: Item
instance of: scholarly article
title: On combinatorics of Schrödinger perturbations
zbMATH Open document ID: 1170.47005
author: Tomasz Jakubowski
published in: Potential Analysis
publication date: 2009-07-24T00:00:00Z
review text: In this paper, the author gives a tight upper bound for Schrödinger-type perturbations of integral kernels. The proofs are based on the identities involving Stirling numbers of the first kind. These results may be of independent interest in the theory of Stirling numbers. Also, the author specializes to transition densities \(p\) and explains that, in this case, the perturbed kernel \(\tilde p\) is a transition density, too, thus allowing for a construction of new semigroups and evolutions. For recent developements in Schrödinger perturbations of time-nonhomogeneous transition probabilties, the reader may refer to [\textit{K.\,Bogdan, W.\,Hansen} and the author, Stud.\ Math.\ 189, No.\,3, 235--254 (2008; Zbl 1161.47009)] and [\textit{A.\,Gulisashvili}, Trans.\ Am.\ Math.\ Soc.\ 360, No.\,8, 4063--4098 (2008; Zbl 1141.47031)].
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 5586415
zbMATH Keywords: Schrödinger perturbations
zbMATH Keywords: transition density
zbMATH Keywords: Stirling numbers
MaRDI profile type: Publication
full work available at URL: s11118-009-9123-y
OpenAlex ID: W2041376195
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DOI: 10.1007/S11118-009-9123-Y
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description: scientific article