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Algebra i Analiz, 1998, Volume 10, Issue 3, Pages 31–44 (Mi aa995)  

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

Research Papers

Lower bounds on the values of an entire function of exponential type at certain integers, in terms of a least superharmonic majorant

P. Koosisa, Henrik L. Pedersenb

a Mathematics Department, McGill University, Montreal, Québec, Canada
b Matematisk Afdeling, Københavns Universitet, København, Denmark

Abstract: In this,paper and the following one, it is shown that if $A<\pi$ and $\eta>0$ is sufficiently small (depending on $A$), the entire functions $f(z)$ of exponential type $\le A$ satisfying $\sum^{\infty}_{m=-\infty}(\log^+|f(n)|/(1+n^2))\le\eta$ form a normal family (in $\mathbb C$). General properties of least superharmonic majorants are used to obtain this result, and from it the multiplier theorem of Beurling and Malliavin is readily derived.

Keywords: Entire function of exponential type, least superharmonic majorant, logarithmic sum, BeurlingT-Malliavin multiplier theorem.

Full text: PDF file (541 kB)

English version:
St. Petersburg Mathematical Journal, 1999, 10:3, 429–439

Bibliographic databases:

Received: 27.10.1997
Language:

Citation: P. Koosis, Henrik L. Pedersen, “Lower bounds on the values of an entire function of exponential type at certain integers, in terms of a least superharmonic majorant”, Algebra i Analiz, 10:3 (1998), 31–44; St. Petersburg Math. J., 10:3 (1999), 429–439

Citation in format AMSBIB
\Bibitem{KooPed98}
\by P.~Koosis, Henrik L.~Pedersen
\paper Lower bounds on the values of an entire function of exponential type at certain integers, in terms of a~least superharmonic majorant
\jour Algebra i Analiz
\yr 1998
\vol 10
\issue 3
\pages 31--44
\mathnet{http://mi.mathnet.ru/aa995}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1628018}
\zmath{https://zbmath.org/?q=an:0920.30021}
\transl
\jour St. Petersburg Math. J.
\yr 1999
\vol 10
\issue 3
\pages 429--439


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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. Pedersen H.L., “Entire functions and logarithmic sums over nonsymmetric sets of the real line”, Annales Academiae Scientiarum Fennicae–Mathematica, 25:2 (2000), 351–388  mathscinet  zmath  isi
    2. Koosis P., “Use of logarithmic sums to estimate polynomials”, Annales Academiae Scientiarum Fennicae–Mathematica, 26:2 (2001), 409–446  mathscinet  zmath  isi
    3. Pedersen H.L., “Estimates of entire functions of exponential type less than $\pi$ in terms of logarithmic sums over real Duffin and Schaeffer sequences”, Potential Anal., 19:3 (2003), 251–260  crossref  mathscinet  zmath  isi  scopus
    4. J. Mashreghi, F. L. Nazarov, V. P. Havin, “Beurling–Malliavin multiplier theorem: the seventh proof”, St. Petersburg Math. J., 17:5 (2006), 699–744  mathnet  crossref  mathscinet  zmath  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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