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Spectral theory and representations of nilpotent groups

Authors: P. Levy-Bruhl, A. Mohamed and 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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Keywords: Representations of nilpotent Lie groups, spectral theory for partial differential equations
Article copyright: © Copyright 1992 American Mathematical Society

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