Bulletin of the American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

Spectral theory and representations of nilpotent groups

Author(s): P. Levy-Bruhl; A. Mohamed; J. Nourrigat
Journal: Bull. Amer. Math. Soc. 26 (1992), 299-303.
MSC (2000): Primary 35P20; Secondary 22E27, 35J10
MathSciNet review: 1129314
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Abstract: 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.

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