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Mat. Sb., 2008, Volume 199, Number 1, Pages 133–160 (Mi msb3882)  

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

Classes of entire functions that are rapidly decreasing on the real axis: theory and applications

A. M. Sedletskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Two types of classes of entire functions ($W_\alpha$ and $Z_\alpha$), which are rapidly decreasing on the real axis are considered. Conditions to ensure that these classes are non-trivial are found and the classes of the corresponding Fourier transforms are described. Results on the classes $Z_\alpha$ are applied to the question of whether a rapidly decreasing function with rapidly decreasing Fourier transform is trivial. This yields not just an extension of Morgan's well-known theorem, but also its converse.
Bibliography: 18 titles.

DOI: https://doi.org/10.4213/sm3882

Full text: PDF file (651 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:1, 131–157

Bibliographic databases:

UDC: 517.547.22+517.443
MSC: Primary 30D15; Secondary 42A38
Received: 11.05.2007 and 08.10.2007

Citation: A. M. Sedletskii, “Classes of entire functions that are rapidly decreasing on the real axis: theory and applications”, Mat. Sb., 199:1 (2008), 133–160; Sb. Math., 199:1 (2008), 131–157

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm3882
  • http://mi.mathnet.ru/eng/msb/v199/i1/p133

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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. I.A. Cheltsov, “Extremal metrics on two Fano varieties”, Sb. Math, 200:1 (2009), 95  mathnet  crossref  mathscinet  zmath  elib  scopus
    2. M. I. Musin, “O prostranstve tselykh funktsii, bystro ubyvayuschikh na veschestvennoi pryamoi”, Ufimsk. matem. zhurn., 4:1 (2012), 136–145  mathnet
    3. A. M. Sedletskii, “Rapid Decrease of Entire Functions along the Real Axis and the Uniqueness of the Fourier-Transform Pair”, Math. Notes, 92:2 (2012), 270–279  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Il’d.K.h. Musin, M.I.. Musin, “On a space of entire functions rapidly decreasing on the real axis and its Fourier transform”, European Journal of Mathematics, 2015  crossref  mathscinet  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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