Logarithmic Terms in Trace Expansions of Atiyah-patodi-singer Problems
نویسندگان
چکیده
Introduction. Let D be a first-order differential operator of Dirac-type from C(X,E1) to C (X,E2) (E1 and E2 Hermitian N -dimensional vector bundles over a compact n-dimensional C ∞ manifold X with boundary ∂X = X ), and let D≥ be the L2-realization defined by the boundary condition Π≥(u|X′) = 0; here Π≥ is the orthogonal projection onto the nonnegative eigenspace for a certain selfadjoint operator A overX ′ entering inD. For ∆B = D ∗ ≥D≥ (and likewise for D≥D ∗ ≥), the following heat trace expansion was shown in a joint work with Seeley [GS95]:
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