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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 2, Pages 393–415 (Mi izv1812)  

This article is cited in 3 scientific papers (total in 3 papers)

On a class of biorthogonal expansions in exponential functions

A. M. Sedletskii


Abstract: We consider a biorthogonal expansion in terms of the system $\{e^{\lambda_nx}\}$, where $\lambda_n$ are the zeros of the entire function
$$ L(z)=h_0e^z+\int_0^1e^{zt}k(t) dt,\qquad h_0\ne0, $$
and $k^{(m)}(t)$ has bounded variation for some integer $m\geqslant0$, $k^{(j)}(0)=0$ for $j=0,1,…,m-1$ and $k^{(m)}(0+0)\ne0$. The function to be expanded has domain $(0,1)$. We describe the sets of convergence (and divergence) of the series for the classes $L^p$, $C$, $\operatorname{Lip}\alpha$, and $V$. The results indicate that the series have properties different from those of ordinary Fourier series; and the difference becomes more pronounced as $m$ increases.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:2, 375–395

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A60, 41A30; Secondary 30A16
Received: 23.12.1975

Citation: A. M. Sedletskii, “On a class of biorthogonal expansions in exponential functions”, Izv. Akad. Nauk SSSR Ser. Mat., 41:2 (1977), 393–415; Math. USSR-Izv., 11:2 (1977), 375–395

Citation in format AMSBIB
\Bibitem{Sed77}
\by A.~M.~Sedletskii
\paper On a~class of biorthogonal expansions in exponential functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 2
\pages 393--415
\mathnet{http://mi.mathnet.ru/izv1812}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=481895}
\zmath{https://zbmath.org/?q=an:0355.42011|0379.42006}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 2
\pages 375--395
\crossref{https://doi.org/10.1070/IM1977v011n02ABEH001725}


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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, “Biorthogonal expansions of functions in series of exponents on intervals of the real axis”, Russian Math. Surveys, 37:5 (1982), 57–108  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. 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
    3. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. I”, Journal of Mathematical Sciences, 129:6 (2005), 4251–4408  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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