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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm1879https://doi.org/10.1070/SM1987v058n02ABEH003107 https://www.mathnet.ru/eng/sm/v172/i3/p335
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Abstract page: | 479 | Russian version PDF: | 178 | English version PDF: | 33 | References: | 63 |
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