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Asymptotics of Dirichlet Spectrum on Some Class of Noncompact Domains
Author(s) -
Parnovski L. B.
Publication year - 1995
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/mana.19951740118
Subject(s) - mathematics , perimeter , manifold (fluid mechanics) , class (philosophy) , dirichlet distribution , pure mathematics , spectrum (functional analysis) , mathematical analysis , boundary (topology) , eigenvalues and eigenvectors , asymptotic formula , boundary value problem , geometry , mechanical engineering , physics , quantum mechanics , artificial intelligence , computer science , engineering
We investigate the asymptotic behaviour of the counting function of Dirichlet eigenvalues on some class of noncompact manifolds. We prove that in cases when the volume or the perimeter (the volume of the boundary) of the manifold is infinite, some additional (nonclassical) terms appear in the precise asymptotics. The coefficients at the classical terms in those are regularized in some special way volume (resp. perimeter) of the manifold.