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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 203–218 (Mi izv1643)  

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

Excesses of systems of exponential functions

A. M. Sedletskii


Abstract: A nonnegative sequence $\{\alpha_n\}$ is called an admissible majorant if the condition $|\lambda_n-\mu_n|\leqslant\alpha_n$, where $\{\lambda_n\}$ and $\{\mu_n\}$ are real regular sequences, implies that the systems of functions $\{\exp(i\lambda_nx)\}$ and $\{\exp(i\mu_nx)\}$ have the same excess in the space $L^2(-a,a)$ ($a<\infty$). A complete characterization of admissible majorants is given for the class of sequences $\alpha_n\downarrow0$ that have the smoothness property $\alpha_{n+1}\sim\alpha_n$. This is used to establish the definitiveness of the author's criterion for the stability of the excess of a system of exponentials in $L^2$.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 191–205

Bibliographic databases:

UDC: 517.5
MSC: Primary 42C30, 41A30; Secondary 30D15
Received: 01.03.1979

Citation: A. M. Sedletskii, “Excesses of systems of exponential functions”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 203–218; Math. USSR-Izv., 16:1 (1981), 191–205

Citation in format AMSBIB
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\by A.~M.~Sedletskii
\paper Excesses of systems of exponential functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 1
\pages 203--218
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=563792}
\zmath{https://zbmath.org/?q=an:0465.42008|0437.42006}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 191--205
\crossref{https://doi.org/10.1070/IM1981v016n01ABEH001288}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LP24600010}


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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. A. M. Sedletskii, “Nonharmonic Fourier series without the Riemann–Lebesgue property”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 545–557  mathnet  crossref  mathscinet  zmath  isi
    2. A. M. Sedletskii, “A construction of complete minimal, but not uniformly minimal, exponential systems with real separable spectrum in $L^p$ and $C$”, Math. Notes, 58:4 (1995), 1084–1093  mathnet  crossref  mathscinet  zmath  isi
    3. B. N. Khabibullin, “Stability of Completeness for Systems of Exponentials on Compact Convex Sets in $\mathbb C$”, Math. Notes, 72:4 (2002), 542–550  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. I”, Journal of Mathematical Sciences, 129:6 (2005), 4251–4408  mathnet  crossref  mathscinet  zmath
    5. A. M. Sedletskii, “On the Stability of the Uniform Minimality of a Set of Exponentials”, Journal of Mathematical Sciences, 155:1 (2008), 170–182  mathnet  crossref  mathscinet  zmath  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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