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Zbl 0706.58073
Guillopé, Laurent
Introduction à l'invariant $\eta$ . (Introduction to the invariant $\eta$ ). (French)
[A] Sémin. Théor. Spectrale Géom. 7, Année 1988-1989, 103-114 (1989).

[For the entire collection see Zbl 0699.00033.] \par Let M be a compact Riemannian manifold, E a Hermitian bundle of finite rank on M and A: $\Gamma$ (E)$\to \Gamma (E)$ a positive pseudo- differential operator with an elliptic and selfadjoint principal symbol. If $\eta\sb A(s)$ is the $\eta$ function which is canonically associated to A, the author proves that it has a meromorphic extension to ${\bbfC}$ which is regular in $s=0$. The paper contains also 57 references on the theory of $\eta$ function.
[M.Puta]

MSC 2000:: *58J50 Spectral problems; spectral geometry; scattering theory
47G30 Pseudodifferential operators
58J40 Pseudodifferential and Fourier integral operators on manifolds
35S05 General theory of pseudodifferential operators
53C55 Complex differential geometry (global)

Keywords: Seeley theorem; eta-function; Riemannian manifold; Hermitian bundle; meromorphic extension

Citations: Zbl 0699.00033

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