Dirichlet and Neumann heat invariants for Euclidean balls

Michael Levitin

doi:10.1016/S0926-2245(97)00016-8

Dirichlet and Neumann heat invariants for Euclidean balls

Michael Levitin

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

Using the theory of heat invariants we present an efficient and economical method of obtaining the higher coefficients of the asymptotic expansion of the trace of the heat semigroup for the Dirichlet and (generalized) Neumann Laplacians acting on an m-dimensional ball. The results are presented in the form of explicit formulae for the first 10 coefficients as functions of m.

Original language	English
Pages (from-to)	35-46
Number of pages	12
Journal	Differential Geometry and its Applications
Volume	8
Issue number	1
DOIs	https://doi.org/10.1016/S0926-2245(97)00016-8
Publication status	Published - Feb 1998

Keywords

Asymplotics
Heat equation
Laplacian
Partition function
Spectral invariants

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10.1016/S0926-2245(97)00016-8

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title = "Dirichlet and Neumann heat invariants for Euclidean balls",

abstract = "Using the theory of heat invariants we present an efficient and economical method of obtaining the higher coefficients of the asymptotic expansion of the trace of the heat semigroup for the Dirichlet and (generalized) Neumann Laplacians acting on an m-dimensional ball. The results are presented in the form of explicit formulae for the first 10 coefficients as functions of m.",

keywords = "Asymplotics, Heat equation, Laplacian, Partition function, Spectral invariants",

author = "Michael Levitin",

year = "1998",

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T1 - Dirichlet and Neumann heat invariants for Euclidean balls

AU - Levitin, Michael

PY - 1998/2

Y1 - 1998/2

N2 - Using the theory of heat invariants we present an efficient and economical method of obtaining the higher coefficients of the asymptotic expansion of the trace of the heat semigroup for the Dirichlet and (generalized) Neumann Laplacians acting on an m-dimensional ball. The results are presented in the form of explicit formulae for the first 10 coefficients as functions of m.

AB - Using the theory of heat invariants we present an efficient and economical method of obtaining the higher coefficients of the asymptotic expansion of the trace of the heat semigroup for the Dirichlet and (generalized) Neumann Laplacians acting on an m-dimensional ball. The results are presented in the form of explicit formulae for the first 10 coefficients as functions of m.

KW - Asymplotics

KW - Heat equation

KW - Laplacian

KW - Partition function

KW - Spectral invariants

UR - http://www.scopus.com/inward/record.url?scp=0031990339&partnerID=8YFLogxK

U2 - 10.1016/S0926-2245(97)00016-8

DO - 10.1016/S0926-2245(97)00016-8

M3 - Article

SN - 0926-2245

VL - 8

SP - 35

EP - 46

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

IS - 1

ER -

Dirichlet and Neumann heat invariants for Euclidean balls

Abstract

Keywords

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