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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Oscillation method in the spectral problem for a fourth order differential operator with a self-similar weight


Author: A. A. Vladimirov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 27 (2015), nomer 2.
Journal: St. Petersburg Math. J. 27 (2016), 237-244
MSC (2010): Primary 34L10, 34L15
DOI: https://doi.org/10.1090/spmj/1385
Published electronically: January 29, 2016
MathSciNet review: 3444462
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Abstract: Selfadjoint boundary problems are considered for the differential equation $ y^{(4)}-\lambda \rho y=0$, where the weight $ \rho \in W_2^{-1}[0,1]$ is the generalized derivative of a self-similar function of the Kantor type. On the basis of the study of oscillation properties of eigenfunctions, the characteristics of the known spectral asymptotics of such problems are refined.


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Additional Information

A. A. Vladimirov
Affiliation: A. A. Dorodnitsyn Computer Center, Russian Academy of Sciences, Vavilova str. 40, 119333 Moscow, Russia
Email: vladimi@mech.math.msu.su

DOI: https://doi.org/10.1090/spmj/1385
Keywords: Differential operator, oscillation of eigenfunctions, self-similar function, spectral asymptotics
Received by editor(s): March 3, 2014
Published electronically: January 29, 2016
Additional Notes: Supported by RFBR (grant no. 13-01-00705)
Article copyright: © Copyright 2016 American Mathematical Society

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