Logarithmic terms in asymptotic expansions of heat operator traces
Titel:
Logarithmic terms in asymptotic expansions of heat operator traces
Auteur:
Gilkey, Peter B. Grubb, Gerd
Verschenen in:
Communications in partial differential equations
Paginering:
Jaargang 23 (1998) nr. 5-6 pagina's 777-792
Jaar:
1998
Inhoud:
Let P be an elliptic selfadjoint positive classical pseudodifferential operator of order d on a compact m-dimensional manifold without boundary. The heat trace of P has an asymptotic expansion in[image omitted] and tk log t for l=0,1,2,... and k=1,2,... We show that the coefficients of all terms in this expansion are non-trivial for a dense set of P. We show that the coefficient of the [image omitted] term is not locally computable when [image omitted] is a positive integer; the ramaining coefficients are known to be locally computable. —Let PB be an operator of Dirac type on a compact n-dimentional commanifold with smooth boundary such that the structures are product near the boundary; here a spectral boundary condition is imposed. Let[image omitted] If n is even, the heat trace of[image omitted] has and asymptotic expansion in[image omitted] and k=0,1,2,...; if n is odd, there is an expansion without the[image omitted] terms. We show that all coefficients (all but one if n is odd) are nontrivial for a dense set of operators.
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