Non-commutative residue of projections in Boutet de Monvel's calculus

2007/09/21 by Anders Gaarde, Gaarde, Anders
Mathematics · #35S15 #58J32 #58J42 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #K-Theory and Homology (math.KT) #Mathematical and Theoretical Analysis #math.AP #math.KT #msc:35S15 #msc:58J32 #msc:58J42

paper · pdf · doi:10.48550/arxiv.0709.3407

10 pages

arxiv created 2007/09/21 · openalex publication_date 2007/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus.

Citations

• Logarithms and sectorial projections for elliptic boundary problems
• The local and global parts of the basic zeta coefficient for operators on manifolds with boundary

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