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Mat. Sb., 1998, Volume 189, Number 3, Pages 125–140 (Mi msb313)  

This article is cited in 4 scientific papers (total in 4 papers)

Approximation properties of exponential systems on the real line and the half-line

A. M. Sedletskii

M. V. Lomonosov Moscow State University

Abstract: For arbitrary $a>0$ and $\alpha >1$ a class of entire functions depending on a complex parameter $\mu$ is constructed. The values of $\mu$ such that the sequence of zeros $\lambda _n$ of a function in this class generates a complete and minimal exponential system
$$ \exp (-i\lambda _nt-a|t|^\alpha ) $$
in $L^p(\mathbb R)$ $(L^p(\mathbb R_+))$, $p\geqslant 2$, are described. Examples of such systems were previously known only for $\alpha=2$.

DOI: https://doi.org/10.4213/sm313

Full text: PDF file (292 kB)
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English version:
Sbornik: Mathematics, 1998, 189:3, 443–460

Bibliographic databases:

UDC: 517.5
MSC: 30B60, 42C30
Received: 30.05.1997

Citation: A. M. Sedletskii, “Approximation properties of exponential systems on the real line and the half-line”, Mat. Sb., 189:3 (1998), 125–140; Sb. Math., 189:3 (1998), 443–460

Citation in format AMSBIB
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\paper Approximation properties of exponential systems on the real line and the half-line
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\yr 1998
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\pages 125--140
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\transl
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\yr 1998
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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, “A necessary condition for the uniform minimality of a system of exponentials in $L^p$ spaces on the line”, Sb. Math., 192:11 (2001), 1721–1740  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. II”, Journal of Mathematical Sciences, 130:6 (2005), 5083–5255  mathnet  crossref  mathscinet  zmath
    3. Popov A.Yu., Sedletskii A.M., “Zeros distribution of Mittag-Leffler functions”, Dokl. Math., 67:3 (2003), 336–339  mathnet  mathscinet  zmath  isi  elib
    4. A. M. Sedletskii, “Nonasymptotic Properties of Roots of a Mittag-Leffler Type Function”, Math. Notes, 75:3 (2004), 372–386  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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