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

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),
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

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
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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
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
3. B.N. Allison, “Models of isotropic simple Lie algebras”, Communications in Algebra, 7:17 (1979), 1835
4. Henrik Winkler, “Spectral Estimations for Can nical Systems”, Math Nachr, 220:1 (2000), 115
5. Aleksey Kostenko, Gerald Teschl, “Spectral Asymptotics for Perturbed Spherical Schrödinger Operators and Applications to Quantum Scattering”, Commun. Math. Phys, 2013
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