Spectral estimates for positive Rockland operators

A.F.M. Elst, ter, D.W. Robinson

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

Let (h,G,U) be an irreducible unitary representation of a homogeneous Lie group G and H a self-adjoint operator on h associated with a positive Rockland operator. We derive upper and lower bounds on the eigenvalue distribution of H in terms of volume estimates on the coadjoint orbit corresponding to the representation U. Hence we deduce bounds on the partition function B -> Trh(exp(-BH)). An application is given to the spectrum and eigenfunctions of the general anharmonic oscillator.
Original languageEnglish
Title of host publicationAlgebraic groups and Lie groups
EditorsG.I. Lehrer
Place of PublicationCambridge
PublisherCambridge University Press
Pages195-213
ISBN (Print)0-521-58532-5
Publication statusPublished - 1997

Publication series

NameAustralian Mathematical Society Lecture Series
Volume9

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