Singular and quasi-bounded functions associated with the heat equation
type: Item
instance of: scholarly article
title: Singular and quasi-bounded functions associated with the heat equation
zbMATH Open document ID: 0632.31007
DOI: 10.1007/BF01160211
author: Bevan Thompson
author: Jan Chabrowski
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173952
review text: We develop a theory of singular and quasi-bounded functions associated with the heat equation. We define quasi-bounded and singular functions by means of an operator S defined on the set of nonnegative functions admitting superthermic majorants. We show that a nonnegative temperature can be expressed as a sum of a quasi-bounded and a singular function. We give explicit formulae for the operator S as the integral of a suitable kernel function with respect to a Borel measure obtained from the Widder, respectively, Kemper representation of nonnegative temperatures. In particular, we show that the singular part of a function arises from the singular part of the representing measure with respect to caloric measure. Also we give some other quasiboundedness criteria and discuss potentials.
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 4027864
zbMATH Keywords: singular and quasi-bounded functions
zbMATH Keywords: nonnegative functions
zbMATH Keywords: superthermic majorants
zbMATH Keywords: nonnegative temperature
zbMATH Keywords: kernel function
zbMATH Keywords: quasi-boundedness
zbMATH Keywords: potentials
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4027864