Statistical de Rham Hodge operators, spectral Einstein functionals and the noncommutative residue

TL;DR

This paper extends spectral functionals and noncommutative residue concepts to noncommutative geometry, proving a key theorem for statistical de Rham Hodge operators on manifolds with boundary.

Contribution

It introduces spectral functionals for noncommutative fields and establishes a Dabrowski-Sitarz-Zalecki type theorem in this context.

Findings

Established a theorem for statistical de Rham Hodge operators on manifolds with boundary.

Extended spectral functionals to noncommutative geometry.

Linked noncommutative residue with boundary value problems.

Abstract

Inspired by statistical de Rham Hodge operators and the spectral functionals, we carry on some promotion to spectral functionals to noncommutative fields, and associate them with the noncommutative residue on manifolds with boundary. We prove the Dabrowski-Sitarz-Zalecki type theorem for statistical de Rham Hodge operators on manifolds with boundary.