An asymptotic expansion for the heat equation

Greiner, Peter

doi:10.1090/pspum/016/0265784

Cited by 152 publications

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“…Greiner [22]), the trace Tr(ϕ 1 e −t ψ 1 ) has the usual expansion as t → 0 in half-integer powers of t. Now our theorem follows directly from Proposition 3.4.…”

Section: Usual Poles Of Relative Zeta Functionsmentioning

confidence: 73%

Zeta regularized determinants for conic manifolds

Loya

McDonald

Park

2007

Journal of Functional Analysis

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We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ -determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant.

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“…Greiner [22]), the trace Tr(ϕ 1 e −t ψ 1 ) has the usual expansion as t → 0 in half-integer powers of t. Now our theorem follows directly from Proposition 3.4.…”

Section: Usual Poles Of Relative Zeta Functionsmentioning

confidence: 73%

Zeta regularized determinants for conic manifolds

Loya

McDonald

Park

2007

Journal of Functional Analysis

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“…The Eq. (2.12) is an immediate consequence of the results in [13,23]. From [8] and the proof of [3,Theorem 4.5], we need only to prove…”

Section: )mentioning

confidence: 88%

A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

2015

manuscripta math.

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In this paper, we extend the Cappell-Miller analytic torsion to manifolds with boundary under the absolute and relative boundary conditions and using the techniques of Brüning-Ma and Su-Zhang, we get the anomaly formula of it for odd dimensional manifolds. Then by the methods of Brüning-Ma, Cappell-Miller and Su-Zhang, we get the CheegerMüller theorem for the Cappell-Miller analytic torsion on odd dimensional manifolds with boundary up to a sign. As a consequence of the main theorem, we get the gluing formula for the Cappell-Miller analytic torsion which generalizes a theorem of Huang.

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“…where the a j ðOÞ; j ¼ 0; 1; 2; y are locally computable geometric invariants of O [6,9]. Let cðOÞ denote the length of the shortest closed periodic geodesic in O: It was conjectured that the behaviour of a j ðOÞ; j-N is related to cðOÞ by formulae (4), (19), (21) in [3].…”

Section: Article In Pressmentioning

confidence: 99%

Asymptotics of the heat exchange

Berg

2004

Journal of Functional Analysis

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Let K be a compact subset in Euclidean space R m ; and let E K ðtÞ denote the total amount of heat in R m \K at time t; if K is kept at fixed temperature 1 for all tX0; and if R m \K has initial temperature 0. For two disjoint compact subsets K 1 and K 2 we define the heat exchange H K1;K2 ðtÞ ¼ E K1 ðtÞ þ E K2 ðtÞ À E K1,K2 ðtÞ: We obtain the leading asymptotic behaviour of H K1;K2 ðtÞ as t-0 under mild regularity conditions on K 1 and K 2 : r

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An asymptotic expansion for the heat equation

Cited by 152 publications

References 0 publications

Zeta regularized determinants for conic manifolds

Zeta regularized determinants for conic manifolds

A Cheeger–Müller theorem for Cappell–Miller torsions on manifolds with boundary

Asymptotics of the heat exchange

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