Remarks on nonlocal trace expansion coefficients

Details Remarks on nonlocal trace expansion coefficients Remarks on nonlocal trace expansion coefficients

2005-10-03

arxiv.org/abs/math/0510041v2

Mathematics

Analysis of PDEs

Minor corrections. To appear in a proceedings volume in honor of K. Wojciechowski, "Analysis and Geometry of Boundary Value Pr

Scientific paper

In a recent work, Paycha and Scott establish formulas for all the Laurent coefficients of Tr(AP^{-s}) at the possible poles. In particular, they show a formula for the zero'th coefficient at s=0, in terms of two functions generalizing, respectively, the Kontsevich-Vishik canonical trace density, and the Wodzicki-Guillemin noncommutative residue density of an associated operator. The purpose of this note is to provide a proof of that formula relying entirely on resolvent techniques (for the sake of possible generalizations to situations where powers are not an easy tool). - We also give some corrections to transition formulas used in our earlier works.

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