Abstract

Let M be a compact Riemannian manifold with smooth boundary ∂M. We study the asymptotic expansions associated with the generalized heat operator Qe^−tP_B with suitable boundary conditions. A new invariant defined on the boundary of M is introduced, and a method is given that relates the heat content asymptotics for the generalized heat operator and the standard heat operator  e^−tP_B with the new boundary asymptotics. As an application, we compute the boundary asymptotics associated with an operator of Laplace type, and the asymptotics for a generalized operator constructed from an operator of Dirac type.

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