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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 3, Pages 469–479 (Mi izv1082)  

This article is cited in 6 scientific papers (total in 6 papers)

On the asymptotic behaviour of the Titchmarsh–Weyl $m$-function

A. A. Danielyan, B. M. Levitan


Abstract: The asymptotic expansion
$$ m(z)=\frac{i}{\sqrt z}+\sum_{k=1}^{n+1}a_k(-z)^{-(k+2)/2}+\varepsilon_n(z),\quad \varepsilon_n(z)=o(|z|^{-(k+3)/2}), $$
valid outside any angle $|{\operatorname{tg}\theta}|<\varepsilon$, $\varepsilon>0$, is obtained for the Weyl–Titchmarsh function of the Sturm-Liouville problem on the half-axis with potential $g(x)\in C^n[0,\delta)$.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:3, 487–496

Bibliographic databases:

UDC: 517.53
MSC: Primary 34B20, 34E05; Secondary 34B25
Received: 26.05.1988

Citation: A. A. Danielyan, B. M. Levitan, “On the asymptotic behaviour of the Titchmarsh–Weyl $m$-function”, Izv. Akad. Nauk SSSR Ser. Mat., 54:3 (1990), 469–479; Math. USSR-Izv., 36:3 (1991), 487–496

Citation in format AMSBIB
\Bibitem{DanLev90}
\by A.~A.~Danielyan, B.~M.~Levitan
\paper On the asymptotic behaviour of the Titchmarsh--Weyl $m$-function
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 3
\pages 469--479
\mathnet{http://mi.mathnet.ru/izv1082}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1072691}
\zmath{https://zbmath.org/?q=an:0723.34038|0712.34072}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..487D}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 3
\pages 487--496
\crossref{https://doi.org/10.1070/IM1991v036n03ABEH002031}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Toru Miyazawa, J Phys A Math Gen, 33:1 (2000), 191  crossref  mathscinet  zmath  isi
    2. Guangsheng Wei, Yan Wang, “Asymptotic behavior for differences of eigenvalues of two Sturm–Liouville problems with smooth potentials”, Journal of Mathematical Analysis and Applications, 377:2 (2011), 659  crossref
    3. Guangsheng Wei, Hong-Kun Xu, “Inverse spectral analysis for the transmission eigenvalue problem”, Inverse Problems, 29:11 (2013), 115012  crossref
    4. Yongxia Guo, Guangsheng Wei, “Inverse Sturm–Liouville problems with the potential known on an interior subinterval”, Applicable Analysis, 2014, 1  crossref
    5. Annemarie Luger, Gerald Teschl, Tobias Wöhrer, “Asymptotics of the Weyl function for Schrödinger operators with measure-valued potentials”, Monatsh Math, 2015  crossref
    6. Toru Miyazawa, “Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation”, J. Math. Phys, 56:4 (2015), 042105  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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