Spanning \(L^{2}\) of a nilpotent Lie group by eigenvectors of invariant differential operators

DOI10.1007/s00209-007-0297-yzbMath1156.22009OpenAlexW2073445495WikidataQ115388813 ScholiaQ115388813MaRDI QIDQ957900

L. Scuto, Jean Ludwig, Carine Molitor-Braun

Publication date: 1 December 2008

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0297-y

zbMATH Keywords

nilpotent Lie groupleft regular representationdisintegration of a representationleft invariant differential operator

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) (L^1)-algebras on groups, semigroups, etc. (43A20)

Cites Work

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• Necessary conditions for local solvability of homogeneous left invariant differential operators on nilpotent Lie groups
• Unitary representation theory of exponential Lie groups
• Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition
• A new criterion for local non-solvability of homogeneous left invariant differential operators on nilpotent Lie groups.
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• FINE DISINTEGRATION OF THE LEFT REGULAR REPRESENTATION
• Non-solvability for a class of left-invariant second-order differential operators on the Heisenberg group

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