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Local Solvability on H_1: Non-homogeneous Operators

By Christopher J. Winfield

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.Comment: 37 pages. Minor corrections in text; results unchanged. Slightly condensed version to appear in Math.

Topics: Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 35R03
Year: 2011
OAI identifier: oai:arXiv.org:1104.5515
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