Measurable operators and the asymptotics of heat kernels and zeta functions

2012/01/17 by Carey, Alan, Sukochev, Fedor
#58B34 (Primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1201.3661

Abstract

In this note we answer some questions inspired by the introduction, by Alain Connes, of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of ζ-functions and heat kernels. The answers have remained elusive for some 15 years.

Related

• The Dixmier trace and asymptotics of zeta functions
• ζ-function and heat kernel formulae
• Heat kernel for non-local operators with variable order
• Heat kernel-zeta function relationship coming from the classical moment problem
• Heat Expansion and Zeta