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The Heat Kernel Expansion

  • J. J. Duistermaat
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

Our operator Q = D 2 , the square of the spin-c Dirac operator, has scalar principal symbol. So for the discussion of the asymptotic expansion of its heat kernel, we may restrict ourselves to the case that Q is a second order differential operator, acting on sections of a complex vector bundle F over a d-dimensional Riemannian manifold (M, β), with principal symbol given by
$$\sigma _{\it{Q}} (\xi)\,=\,\beta ^{-1}\,(\xi,\,\xi)\, \cdot \,1,\,\,\,\,\xi\,\in\,\rm{T}^{*}\,\it{M}.$$
(8.1)

Keywords

Asymptotic Expansion Heat Kernel Formal Power Series Geodesic Distance Integral Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • J. J. Duistermaat
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

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