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Mat. Zametki, 1977, Volume 22, Issue 6, Pages 803–814 (Mi mz8102)  

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

Excesses of systems of exponential functions

A. M. Sedletskii

Moscow Power Engineering Institute

Abstract: Conditions on the closeness of real sequences $\{\lambda_n\}$ and $\{\mu_n\}$ are studied which imply the equality of the excesses of the systems $\{\exp(i\lambda_nx)\}$ and $\{\exp(i\lambda_nx)\}$ in the space $L^2(-a,a)$. A theorem is formulated in terms of the difference of the sequences $\{\lambda_n\}$ and $\{\mu_n\}$ enumerating the functions. In the corollaries of the theorem, conditions are given in terms of the behavior of the difference $\lambda_n-\mu_n$. An example is constructed showing that the condition $\lambda_n-\mu_n\to0$ alone is not sufficient for equality of the excesses.

Full text: PDF file (768 kB)

English version:
Mathematical Notes, 1977, 22:6, 941–947

Bibliographic databases:

UDC: 517.5
Received: 30.09.1975

Citation: A. M. Sedletskii, “Excesses of systems of exponential functions”, Mat. Zametki, 22:6 (1977), 803–814; Math. Notes, 22:6 (1977), 941–947

Citation in format AMSBIB
\Bibitem{Sed77}
\by A.~M.~Sedletskii
\paper Excesses of systems of exponential functions
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 6
\pages 803--814
\mathnet{http://mi.mathnet.ru/mz8102}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=477593}
\zmath{https://zbmath.org/?q=an:0375.42007}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 6
\pages 941--947
\crossref{https://doi.org/10.1007/BF01099562}


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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, “Excesses of systems of exponential functions”, Math. USSR-Izv., 16:1 (1981), 191–205  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. I”, Journal of Mathematical Sciences, 129:6 (2005), 4251–4408  mathnet  crossref  mathscinet  zmath
    4. Zikkos, E, “On the excess of complex exponential systems in L-2(-a, a)”, Journal of Mathematical Analysis and Applications, 308:1 (2005), 47  crossref  isi
    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
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