Matrix parameterized pseudo-differential calculi on modulation spaces

TL;DR

This paper extends the continuity properties of classical pseudo-differential calculi, specifically Shubin's family, to a broader matrix-parameterized family within the modulation space framework, enhancing understanding of their analytical behavior.

Contribution

It introduces a generalized matrix-parameterized family of pseudo-differential calculi and proves that continuity properties extend from the classical to this broader family.

Findings

Continuity properties extend to the matrix-parameterized family.

The broader family includes Shubin's classical calculi as special cases.

Results enhance the analytical understanding of these operators on modulation spaces.

Abstract

We consider a broad matrix parameterized family of pseudo-differential calculi, containing the usual Shubin's family of pseudo-differential calculi, parameterized by real numbers. We show that continuity properties in the framework of modulation space theory, valid for the Shubin's family extend to the broader matrix parameterized family of pseudo-differential calculi.