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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 1, Pages 154–184 (Mi izv1925)  

This article is cited in 5 scientific papers (total in 5 papers)

Integral characteristics of the growth of spectral functions for generalized second order boundary problems with boundary conditions at a regular end

I. S. Kats


Abstract: For the spectral function $\tau(\lambda)$ of the generalized second order boundary problem
\begin{gather*} -\frac d{dM(x)}[y'_-(x)-\int_{-0}^{x-0}y(s) dQ(s)]-\lambda y(x)=0\qquad(0\leq x<L),
y'_-(0)=m,\qquad y(0)=n, \end{gather*}
and for the function $\eta(\lambda)$, which may belong to an extremely large class of positive functions that are nonincreasing on $[1,+\infty)$, the problem of characterizing the growth of the function $\tau(\lambda)$ as $\lambda\uparrow+\infty$ and of the convergence of the integral $\int^{+\infty}\eta(\lambda) d\tau(\lambda)$ is connected with the behavior as $x\downarrow0$ of the function $M(x)$.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:1, 161–191

Bibliographic databases:

UDC: 517.9
MSC: Primary 34B25; Secondary 34B15
Received: 25.03.1969

Citation: I. S. Kats, “Integral characteristics of the growth of spectral functions for generalized second order boundary problems with boundary conditions at a regular end”, Izv. Akad. Nauk SSSR Ser. Mat., 35:1 (1971), 154–184; Math. USSR-Izv., 5:1 (1971), 161–191

Citation in format AMSBIB
\Bibitem{Kat71}
\by I.~S.~Kats
\paper Integral characteristics of the growth of spectral functions for generalized second order boundary problems with boundary conditions at a regular end
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 1
\pages 154--184
\mathnet{http://mi.mathnet.ru/izv1925}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=276530}
\zmath{https://zbmath.org/?q=an:0276.34016}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 1
\pages 161--191
\crossref{https://doi.org/10.1070/IM1971v005n01ABEH001028}


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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. I. S. Kats, “Generalization of an asymptotic formula of V. A. Marchenko for spectral functions of a second-order boundary value problem”, Math. USSR-Izv., 7:2 (1973), 424–438  mathnet  crossref  mathscinet  zmath
    2. O. D. Apyshev, M. Otelbaev, “On the spectrum of a class of differential operators and some imbedding theorems”, Math. USSR-Izv., 15:1 (1980), 1–24  mathnet  crossref  mathscinet  zmath  isi
    3. B.N. Allison, “Models of isotropic simple Lie algebras”, Communications in Algebra, 7:17 (1979), 1835  crossref
    4. Henrik Winkler, “Spectral Estimations for Can nical Systems”, Math Nachr, 220:1 (2000), 115  crossref  mathscinet  zmath
    5. Aleksey Kostenko, Gerald Teschl, “Spectral Asymptotics for Perturbed Spherical Schrödinger Operators and Applications to Quantum Scattering”, Commun. Math. Phys, 2013  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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