Local Solvability on H₁: Non-homogeneous Operators

2011/04/28 by Christopher J. Winfield, Winfield, Christopher J.
Mathematics · Physics and Astronomy · #35R03 #Advanced Algebra and Geometry #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Waves and Solitons #math.AP #math.CA #msc:35R03

paper · pdf · doi:10.48550/arxiv.1104.5515

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

openalex publication_date 2011/04/28 · arxiv created 2011/10/11 · arxiv updated 2011/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Local solvability and non-solvability are classified for left-invariant differential operators on the Heisenberg group H₁ 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= ∂_x, Y=∂_y+x∂_w on R³. We extend previous studies of operators of the form P_n(X,Y) via representations involving ordinary differential operators with a parameter.

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