Asymptotic expansions for the heat content
type: Item
instance of: scholarly article
title: Asymptotic expansions for the heat content
zbMATH Open document ID: 0940.58020
published in: Pacific Journal of Mathematics
publication date: 2000-07-17T00:00:00Z
review text: Let \(\beta\) be a bounded operator and \(B_\beta\) the operator satisfying the boundary operator condition determined by \(\beta f=0.\) The author uses spectral theory to express the heat content in terms of the spectral resolution of the operator \(B_\beta\) and to relate the asymptotics with a suitably modified zeta function. Then it is shown how the Mellin transform and the properties of the zeta function can be used to obtain the heat content asymptotics for a generalized heat operator. The author introduces the heat content on the boundary and develops some of its properties. She also computes the asymptotics for the boundary invariant when \(B_\beta\) is an operator of Laplace type with Dirichlet and Neumann boundary conditions. Using the above results it is possible to compute the generalized heat content asymptotics for an operator of Dirac type.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J37
zbMATH DE Number: 1344246
zbMATH Keywords: heat content
zbMATH Keywords: generalized heat content asymptotics
zbMATH Keywords: operators of Dirac type
author: S. J. Desjardins
reviewed by: Maria Alessandra Ragusa
MaRDI profile type: Publication
full work available at URL: pjm.1998.183.279
OpenAlex ID: W2057850908
Wikidata QID: Q114606739
DOI: 10.2140/PJM.1998.183.279
description: scientific article; zbMATH DE number 1344246