Bi-invariant Schwartz multipliers and local solvability on nilpotent Lie groups

DOI10.1090/S0273-0979-1988-15647-9zbMath0658.22002OpenAlexW2053108423WikidataQ115282547 ScholiaQ115282547MaRDI QIDQ3807445

J. W. Jenkins

Publication date: 1988

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1988-15647-9

zbMATH Keywords

Fourier transformSchwartz spacetopological algebrairreducible unitary representationsimply connected nilpotent Lie groupKirillov orbitlocal solvability of left invariant differential operators

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Analysis on real and complex Lie groups (22E30) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Cites Work

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• Tempered distributions on Heisenberg groups whose convolution with Schwartz class functions is Schwartz class
• On a connection between nilpotent groups and oscillatory integrals associated to singularities
• Solvability of certain left invariant differential operators by nilmanifold theory

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