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Mathematics of the USSR-Sbornik, 1987, Volume 58, Issue 2, Pages 337–349
DOI: https://doi.org/10.1070/SM1987v058n02ABEH003107
(Mi sm1879)
 

This article is cited in 11 scientific papers (total in 11 papers)

Summability of the logarithm of an almost analytic function and a generalization of the Levinson–Cartwright theorem

A. L. Vol'berg, B. Jöricke
References:
Abstract: This paper is devoted to a generalization of a classical inequality: let $f$ be bounded and analytic in the disk $D$; then $f\not\equiv0\Rightarrow\int_{\mathrm{Fr}\mathbf D}\log|f(e^{i\theta})|\,d\theta>-\infty$, in the case of nonanalytic functions $f$. More precisely, it is proved that if $f=f_1+f_2$, where $f_1$ is the boundary function of a function of bounded characteristic, and $f_2$ is a function in a quasianalytic class (defined by some condition of regularity of decrease of its Fourier coefficients), then $\int_{\mathrm{Fr}\mathbf D}\log|f(e^{i\theta})|\,d\theta>-\infty$. The proof of this result depends in an essential way on a theorem of Levinson and Cartwright. At the same time, the result strengthens the Levinson–Cartwright theorem.
Bibliography: 7 titles.
Received: 25.06.1985
Bibliographic databases:
UDC: 517.5
Language: English
Original paper language: Russian
Citation: A. L. Vol'berg, B. Jöricke, “Summability of the logarithm of an almost analytic function and a generalization of the Levinson–Cartwright theorem”, Math. USSR-Sb., 58:2 (1987), 337–349
Citation in format AMSBIB
\Bibitem{VolJor86}
\by A.~L.~Vol'berg, B.~J\"oricke
\paper Summability of the logarithm of an almost analytic function and a~generalization of the Levinson--Cartwright theorem
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 337--349
\mathnet{http://mi.mathnet.ru//eng/sm1879}
\crossref{https://doi.org/10.1070/SM1987v058n02ABEH003107}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=865765}
\zmath{https://zbmath.org/?q=an:0644.30020}
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  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:479
    Russian version PDF:178
    English version PDF:33
    References:63
     
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