REMARKS ON NONLOCAL TRACE EXPANSION COEFFICIENTS

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.