|
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
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
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
Linking options:
https://www.mathnet.ru/eng/sm3788https://doi.org/10.1070/SM2006v197n11ABEH003813 https://www.mathnet.ru/eng/sm/v197/i11/p13
|
Statistics & downloads: |
Abstract page: | 1274 | Russian version PDF: | 424 | English version PDF: | 38 | References: | 57 | First page: | 5 |
|