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A Laurent expansion for regularized integrals of holomorphic symbols. (English) Zbl 1125.58009
The authors consider a holomorphic family of classical pseudodifferential operators $$A(z)$$ on a compact manifold, for $$z$$ in a domain $$W\subset\mathbb C$$, with holomorphic order $$m:W\to\mathbb C$$. In the asymptotic expansion of the symbol, beside homogeneous terms, log-terms are also included. The authors give an exact formula for all the coefficients in the Laurent expansion of trace $$(A(z))$$ around each pole, in terms of locally defined canonical trace and residue densities. Different results are recaptured and generalized, concerning in particular the so-called Wodzicki non-commutative residue and the Kontsevich-Vishik canonical trace, cf. M. Lesch [Ann. Global Anal. Geom. 17, No. 2, 151–187 (1998; Zbl 0920.58047)].

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J42 Noncommutative global analysis, noncommutative residues 47G30 Pseudodifferential operators
##### Keywords:
non-commutative residue
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