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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 422–436 (Mi izv2255)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalization of an asymptotic formula of V. A. Marchenko for spectral functions of a second-order boundary value problem

I. S. Kats


Abstract: It is established that the spectral functions $\tau(\lambda)$ of the second-order boundary value problem
\begin{gather*} -\frac d{dM(x)}[y^-(x)-\int_{-0}^{x-0}y(s) dQ(s)]-\lambda y(x)=0\qquad(0\le x<L),
y^-(0)=m,\qquad y(0)=n, \end{gather*}
possess power asymptotics $\tau(\lambda)\sim C\lambda^\nu$ as $\lambda\uparrow+\infty$, when the function $M(x)$ possesses power asymptotics as $x\downarrow0$. A partial converse of this fact is also obtained.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 424–438

Bibliographic databases:

UDC: 517.9
MSC: 34B25
Received: 30.12.1971

Citation: I. S. Kats, “Generalization of an asymptotic formula of V. A. Marchenko for spectral functions of a second-order boundary value problem”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 422–436; Math. USSR-Izv., 7:2 (1973), 424–438

Citation in format AMSBIB
\Bibitem{Kat73}
\by I.~S.~Kats
\paper Generalization of an asymptotic formula of V.\,A.~Marchenko for spectral functions of a~second-order boundary value problem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 422--436
\mathnet{http://mi.mathnet.ru/izv2255}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=331116}
\zmath{https://zbmath.org/?q=an:0306.34024}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 424--438
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001947}


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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. Aleksey Kostenko, Gerald Teschl, “Spectral Asymptotics for Perturbed Spherical Schrödinger Operators and Applications to Quantum Scattering”, Commun. Math. Phys, 2013  crossref
    2. I. S. Kats, “Power Asymptotics of Spectral Functions of Boundary Value Problems for Generalized Second-Order Differential Equations with Boundary Conditions at a Singular Endpoint”, Funct. Anal. Appl., 49:1 (2015), 67–71  mathnet  crossref  crossref  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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