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Semiclassical Spectral Asymptotics on Foliated Manifolds

✍ Scribed by Yuri A. Kordyukov

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 309 KB
Volume: 245
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200211)245:1<104::aid-mana104>3.0.co;2-e

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✦ Synopsis

We consider a (hypo)elliptic pseudodifferential operator A h on a closed foliated manifold (M, F), depending on a parameter h > 0, of the form A h = A + h m B, where A is a formally self-adjoint tangentially elliptic operator of order µ > 0 with the nonnegative principal symbol and B is a formally self-adjoint classical pseudodifferential operator of order m > 0 on M with the holonomy invariant transversal principal symbol such that its principal symbol is positive, if µ < m, and its transversal principal symbol is positive, if µ ≥ m. We prove an asymptotic formula for the eigenvalue distribution function N h (λ) of the operator A h when h tends to 0 and λ is constant.

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