[Authors]
 Rastegaev, N. V.

[Title]
 On spectral asymptotics of the Neumann problem for the Sturm-Liouville
 equation with self-similar generalized Cantor type weight

[AMS Subj-class]
 34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
 34B09 Boundary eigenvalue problems
 26A30 Singular functions, Cantor functions, functions with other special properties

[Abstract]
 Spectral asymptotics of the Neumann problem for the Sturm-Liouville equation 
 with generalized derivative of a self-similar generalized Cantor type function 
 as a weight are considered. The spectrum is shown to have a periodicity 
 property for a wide class of Cantor type self-similar functions, and also the 
 weaker "quasi-periodicity" condition is demonstrated under certain mixed 
 boundary conditions. This allows for a more precise description of the main 
 term of the asymptotics of the counting function of eigenvalues. Previous 
 results by A. A. Vladimirov, I. A. Sheipak are generalized.

[Comments]
 LaTeX, Russian, 9 pp.

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