The Heat Kernel Expansion

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


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
$$\sigma _{\it{Q}} (\xi)\,=\,\beta ^{-1}\,(\xi,\,\xi)\, \cdot \,1,\,\,\,\,\xi\,\in\,\rm{T}^{*}\,\it{M}.$$


Asymptotic Expansion Heat Kernel Formal Power Series Geodesic Distance Integral Kernel 
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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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