Local Solvability on H_1: Non-homogeneous Operators

TL;DR

This paper classifies local solvability and non-solvability of certain left-invariant differential operators on the Heisenberg group H_1, extending previous work through representation methods involving ordinary differential operators with parameters.

Contribution

It introduces a classification framework for local solvability of non-homogeneous operators on H_1, extending prior results to more general operators with lower order terms.

Findings

Classification of local solvability and non-solvability for the operators

Extension of previous studies to non-homogeneous operators

Representation involving ordinary differential operators with a parameter

Abstract

Local solvability and non-solvability are classified for left-invariant differential operators on the Heisenberg group H_1 of the form L=P_n(X,Y)+Q(X,Y) where the P_n are certain homogeneous polynomials of order n greater than or equal to 2 and Q is of lower order with X= \partial_x, Y=\partial_y+x\partial_w on R^3. We extend previous studies of operators of the form P_n(X,Y) via representations involving ordinary differential operators with a parameter.