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Sbornik: Mathematics, 2006, Volume 197, Issue 11, Pages 1569–1586
DOI: https://doi.org/10.1070/SM2006v197n11ABEH003813 (Mi sm3788) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Self-similar functions in $L_2[0,1]$ and the Sturm–Liouville problem with singular indefinite weight

A. A. Vladimirov, I. A. Sheipak

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (351 kB) Citations (26)
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DOI: https://doi.org/10.1070/SM2006v197n11ABEH003813
Abstract: The question of the asymptotic behaviour of the spectrum of the boundary value problem
\begin{equation*} -y''-\lambda\rho y=0, \qquad y(0)=y(1)=0, \end{equation*}
is considered, where $\rho$ is a function in $\mathring W_2^{-1}[0,1]$ with arithmetically self-similar primitive function. It is not assumed here that the weight $\rho$ has a constant sign. The theoretical results obtained are illustrated by the data of numerical calculations.
Bibliography: 10 titles.
Received: 16.06.2004 and 21.06.2006
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 11, Pages 13–30
DOI: https://doi.org/10.4213/sm3788
Bibliographic databases:
UDC: 517.984
MSC: Primary 34B25, 47B50; Secondary 47E05
Language: English
Original paper language: Russian
Citation: A. A. Vladimirov, I. A. Sheipak, “Self-similar functions in $L_2[0,1]$ and the Sturm–Liouville problem with singular indefinite weight”, Mat. Sb., 197:11 (2006), 13–30; Sb. Math., 197:11 (2006), 1569–1586
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
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