Dixmier traces for discrete pseudo-differential operators

2019/11/10 by Duván Cardona, Cardona, Duván, César del Corral +3 · 1 citation
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Spectral Theory (math.SP) #math.FA #math.OA #math.SP

paper · pdf · doi:10.48550/arxiv.1911.03924

10 pages. Dedicated to Professor Lázaro Recht on his 79 birthday

arxiv created 2020/03/10 · arxiv updated 2020/03/11

Abstract

In this paper we provide sharp results for the Dixmier traceability of discrete pseudo-differential operators on ℓ²(ℤⁿ). In this setting, we introduce a suitable notion of a class of classical symbols which provide a class of Dixmier traceable discrete pseudo-differential operators. We also present a formula for the Dixmier trace of a Dixmier traceable discrete pseudo-differential operator by using the Connes equivalence between the Wodzicki residue and the Dixmier trace.

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