On partially hypoelliptic operators. Part II: Pseudo differential operators

TL;DR

This paper extends the theory of partially hypoelliptic differential operators to pseudodifferential operators, introducing symbol ideals and topologies to facilitate this generalization.

Contribution

It generalizes the class of partially hypoelliptic operators to pseudodifferential operators using symbol ideals and topology considerations.

Findings

Established symbol ideals on the set of lineality.

Discussed suitable topologies for the generalization.

Extended hypoelliptic operator theory to pseudodifferential operators.

Abstract

This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow the generalizations.