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Levy-Bruhl, P.; Mohamed, A.; Nourrigat, J.

Spectral theory and representations of nilpotent groups. (English) Zbl 0749.35030

Bull. Am. Math. Soc., New Ser. 26, No. 2, 299-303 (1992).
(Authors’ summary:) We give an estimate of the number \(N(\lambda)\) of eigenvalues \(<\lambda\) for the image under an irreducible representation of the “sublaplacian” on a stratified nilpotent Lie algebra. We also give an estimate for the trace of the heat-kernel associated with this operator. The estimates are formulated in term of geometrical objects related to the representation under consideration. An important particular case is the Schrödinger equation with polynomial electrical and magnetical fields.
Reviewer: P.Hillion

Cited in 4 Documents

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)

Keywords:

trace of the heat-kernel; Schrödinger equation
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References:

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