Abstract:
The zeta and eta functions of a differential operator of Dirac-type on a compact n-dimensional manifold, provided with a well-posed pseudodifferential boundary condition, have been shown in [G99] to be meromorphic on ℂ with simple or double poles on the real axis. Extending results from [G99] we show how perturbations of the boundary condition of order −J affect the poles; in particular they preserve a possible regularity of zeta at 0 and a possible simple pole of eta at 0 when J≥n. This applies to perturbations of spectral boundary conditions, also when the structure is non-product and the problem is non-selfadjoint.
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Received: 4 October 1999 / Accepted: 7 July 2000
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Grubb, G. Poles of Zeta and Eta Functions for Perturbations¶of the Atiyah–Patodi–Singer Problem. Commun. Math. Phys. 215, 583–589 (2001). https://doi.org/10.1007/PL00005544
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DOI: https://doi.org/10.1007/PL00005544