Solvability of second-order PDOs on nilpotent groups -- a survey of recent results

DOI10.1007/BF02921324zbMath0840.22018OpenAlexW2070297729MaRDI QIDQ1315479

Fulvio Ricci, Detlef Müller

Publication date: 11 March 1996

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921324

zbMATH Keywords

Heisenberg groupsolvabilitynilpotent groupsspectral analysisunitary operatorssub-Laplacianlocal solvabilityconstant coefficient operatorssecond order linear partial differential operators

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25)

Related Items (4)

Solvability for a class of non-homogeneous differential operators on two-step nilpotent groups ⋮ Another example in the solvability theory of pdo's with double characteristics ⋮ Sulla risolubilita' degli operatori differenziali invarianti sul gruppo di Heisenberg ⋮ Local solvability of partial differential operators on the Heisenberg group

Cites Work

• An example on the Heisenberg group related to the Lewy operator
• Local solvability of second order differential operators on nilpotent Lie groups
• Analysis of second order differential operators on Heisenberg groups. I
• Hypoelliptic differential operators and nilpotent groups
• Analysis of second order differential operators on Heisenberg groups. II
• Solvability for a class of doubly characteristic differential operators on 2-step nilpotent groups
• Hypoelliptic second order differential equations
• Harmonic integrals on strongly pseudo-convex manifolds. I
• A new criterion for local non-solvability of homogeneous left invariant differential operators on nilpotent Lie groups.
• Twisted convolutions with Calderón-Zygmund kernels.
• Harmonic Analysis in Phase Space. (AM-122)
• Calculus on Heisenberg Manifolds. (AM-119)
• Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the -neumann problem
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