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Tr. Mat. Inst. Steklova, 2006, Volume 255, Pages 88–98 (Mi tm255)  

This article is cited in 12 scientific papers (total in 12 papers)

Indefinite Sturm–Liouville Problem for Some Classes of Self-similar Singular Weights

A. A. Vladimirov, I. A. Sheipak

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We continue studying the asymptotics of the spectrum for the boundary value problem $-y"-\lambda \rho y=0$, $y(0)=y(1)=0$, where $\rho $ is a function in the space $\mathring W_{2}^{-1}[0,1]$ with a self-similar primitive. The cases of nonarithmetic and degenerate arithmetic self-similarity of such a primitive are considered.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 255, 82–91

Bibliographic databases:

UDC: 517.984
Received in November 2005

Citation: A. A. Vladimirov, I. A. Sheipak, “Indefinite Sturm–Liouville Problem for Some Classes of Self-similar Singular Weights”, Function spaces, approximation theory, and nonlinear analysis, Collected papers, Tr. Mat. Inst. Steklova, 255, Nauka, MAIK Nauka/Inteperiodika, M., 2006, 88–98; Proc. Steklov Inst. Math., 255 (2006), 82–91

Citation in format AMSBIB
\by A.~A.~Vladimirov, I.~A.~Sheipak
\paper Indefinite Sturm--Liouville Problem for Some Classes of Self-similar Singular Weights
\inbook Function spaces, approximation theory, and nonlinear analysis
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2006
\vol 255
\pages 88--98
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 255
\pages 82--91

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    This publication is cited in the following articles:
    1. A. A. Vladimirov, “Calculating the eigenvalues of the Sturm–Liouville problem with a fractal indefinite weight”, Comput. Math. Math. Phys., 47:8 (2007), 1295–1300  mathnet  crossref  mathscinet  elib  elib
    2. I. A. Sheipak, “Singular points of a self-similar function of spectral order zero: self-similar Stieltjes string”, Math. Notes, 88:2 (2010), 275–286  mathnet  crossref  crossref  mathscinet  isi
    3. A. A. Vladimirov, I. A. Sheipak, “Asymptotics of the Eigenvalues of the Sturm–Liouville Problem with Discrete Self-Similar Weight”, Math. Notes, 88:5 (2010), 637–646  mathnet  crossref  crossref  mathscinet  isi
    4. Sheipak I.A., “O spektre operatora yakobi s eksponentsialno rastuschimi matrichnymi elementami”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 6, 15–21  mathscinet  zmath  elib
    5. N. V. Gaganov, I. A. Sheipak, “A boundedness criterion for the variations of self-similar functions”, Siberian Math. J., 53:1 (2012), 55–71  mathnet  crossref  mathscinet  isi
    6. Nazarov A.I., Sheipak I.A., “Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes”, Bull. Lond. Math. Soc., 44:1 (2012), 12–24  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. A. Vladimirov, I. A. Sheipak, “On the Neumann Problem for the Sturm–Liouville Equation with Cantor-Type Self-Similar Weight”, Funct. Anal. Appl., 47:4 (2013), 261–270  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. I. A. Sheipak, “Asymptotics of the Spectrum of a Differential Operator with the Weight Generated by the Minkowski Function”, Math. Notes, 97:2 (2015), 289–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. A. A. Vladimirov, “Nekotorye zamechaniya ob integralnykh kharakteristikakh vinerovskogo protsessa”, Dalnevost. matem. zhurn., 15:2 (2015), 156–165  mathnet  elib
    10. J. V. Tikhonov, I. A. Sheipak, “On the string equation with a singular weight belonging to the space of multipliers in Sobolev spaces with negative index of smoothness”, Izv. Math., 80:6 (2016), 1242–1256  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. A. S. Ivanov, A. M. Savchuk, “Trace of Order $(-1)$ for a String with Singular Weight”, Math. Notes, 102:2 (2017), 164–180  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. A. A. Vladimirov, “On a class of singular Sturm–Liouville problems”, Trans. Moscow Math. Soc., 80 (2019), 211–219  mathnet  crossref  elib
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