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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)].

58J40 Pseudodifferential and Fourier integral operators on manifolds
58J42 Noncommutative global analysis, noncommutative residues
47G30 Pseudodifferential operators
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