On a weak Lie type for vectors

TL;DR

This paper explores a new weak Lie type structure for vectors within the symbol space of differential operators, focusing on coordinate changes and properties like P-convexity for hypoelliptic operators.

Contribution

It introduces a novel scalar type for local coordinate transformations using vector valued distributions, advancing the understanding of hypoelliptic operators.

Findings

Establishes a scalar type for coordinate change in symbol space

Analyzes P-convexity in the context of hypoelliptic operators

Provides insights into vector valued distributions in differential operator theory

Abstract

In the symbol space for differential operators, we discuss a scalar type for change of local coordinates, using vector valued distributions. In particular, we discuss P-convexity for hypoelliptic operators.