Symbolic computation of DeWitt-Seeley-Gilkey coefficients on curved manifolds
type: Item
instance of: scholarly article
title: Symbolic computation of DeWitt-Seeley-Gilkey coefficients on curved manifolds
zbMATH Open document ID: 0811.58057
author: V. P. Gusynin
author: Vladimir V. Kornyak
published in: Journal of Symbolic Computation
publication date: 1995-05-03T00:00:00Z
review text: Let \(M\) be an \(n\)-dimensional compact curved manifold with a torsion and let \(A\) be a positive elliptic differential operator of order \(2r\) on \(M\). Consider the asymptotic expansion, \(\langle x \mid e^{-tA} x \rangle \sim \sum E_ m(x | A) t^{(m - n)/2r}\), \(m \geq 0\), \(t \to +0\). The functions \(E_ m\) are called DeWitt-Seely-Gilkey coefficients. Using the Widom covariant symbolic calculus for pseudodifferential operators, the authors give an algorithm of computing the coefficients \(E_ m\). Some examples are provided.
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 638320
zbMATH Keywords: heat kernel
zbMATH Keywords: asymptotics
zbMATH Keywords: closed manifold
zbMATH Keywords: elliptic differential operator
zbMATH Keywords: coefficients
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
full work available at URL: jsco.1994.1018
OpenAlex ID: W2002729242
DOI: 10.1006/JSCO.1994.1018
description: scientific article; zbMATH DE number 638320