Zeta and eta functions for Atiyah-Patodi-Singer operators

  • Gerd Grubb
  • Robert T. Seeley


This paper concerns Dirac-type operatorsP on manifoldsX with boundary which are “product-type” near the boundary. That is,\(P = \sigma \left( {\frac{\partial }{{\partial x_n }} + A} \right)\) for a unitary morphism σ and a self-adjoint first-order operatorA onbdry(X);x n denotes the normal coordinate. For a realizationP B defined by a boundary operatorB of Atiyah-Patodi-Singer type, the paper gives a complete description of the singularities of the traces of the meromorphic continuations of Γ(s)D i )s and Γ(s)DP i )s where Δ1 =P B * P B , Δ2 =P B P B * , andD is any differential operator onX which is tangential and independent of 4x n nearbdry(X). This implies expansions for the associated heat kernels and resolvents, containing the usual powers (with both “local” and “global” coefficients) together with logarithmic terms.


Differential Operator Vector Bundle Power Function Zeta Function Pseudodifferential Operator 
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Copyright information

© Mathematica Josephina, Inc. 1996

Authors and Affiliations

  • Gerd Grubb
    • 1
    • 2
  • Robert T. Seeley
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of CopenhagenDenmark
  2. 2.Department of MathematicsUniversity of Massachussetts at BostonUSA

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