Resolvent trace asymptotics for operators in the Shubin class

TL;DR

This paper introduces a new pseudodifferential calculus for Shubin operators, constructs their resolvents, and derives trace expansions, advancing the understanding of spectral properties of these operators.

Contribution

It develops a novel Shubin-type pseudodifferential calculus including parameter-dependent operators and derives resolvent trace asymptotics.

Findings

Constructed resolvents for Shubin-type pseudodifferential operators.

Derived trace expansion formulas for these resolvents.

Enhanced spectral analysis tools for operators in the Shubin class.

Abstract

A new pseudodifferential calculus of Shubin type is introduced. The calculus contains operators depending on a non negative real parameter as well as operators independent of the parameter. Resolvents of Shubin type pseudodifferential operators are constructed and their trace expansion is obtained.