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Semiclassical Spectral Asymptotics on Foliated Manifolds
Author(s) -
Kordyukov Yuri A.
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200211)245:1<104::aid-mana104>3.0.co;2-e
Subject(s) - mathematics , holonomy , semiclassical physics , elliptic operator , transversal (combinatorics) , eigenvalues and eigenvectors , operator (biology) , pure mathematics , mathematical analysis , manifold (fluid mechanics) , invariant (physics) , symbol (formal) , mathematical physics , quantum mechanics , chemistry , physics , mechanical engineering , biochemistry , repressor , computer science , transcription factor , engineering , quantum , gene , programming language
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 pseudodi.erential 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.