Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems

Details Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems

2003-02-24

arxiv.org/abs/math/0302289v2

Ann.Global Analysis Geom. 24: 1-51, 2003

Mathematics

Analysis of PDEs

Published. Abstract added, small typos corrected

Scientific paper

For a Dirac-type operator D with a spectral boundary condition, the associated heat operator trace has an expansion in powers and log-powers of t. Some of the log-coefficients vanish in the Atiyah-Patodi-Singer product case. We here investigate the effect of perturbations of D, by use of a pseudodifferential parameter-dependent calculus for boundary problems. It is shown that the first k log-terms are stable under perturbations of D vanishing to order k at the boundary (and the nonlocal power coefficients behind them are only locally perturbed). For perturbations of D from the APS product case by tangential operators commuting with the tangential part A, all the log-coefficients vanish if the dimension is odd.

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