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 Mat. Sb. (N.S.), 1974, Volume 95(137), Number 1(9), Pages 3–18 (Mi msb3738)

Existence of a basis in the space of functions analytic in the disk, and some properties of Franklin's system

S. V. Bochkarev

Abstract: It is shown that there is a basis in the space of functions analytic in the unit disk and continuous in the closed unit disk. This answers a question posed by Banach. It is further shown that the Franklin system is an unconditional basis in the spaces $L_p(0,1)$ for $1<p<\infty$.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 24:1, 1–16

Bibliographic databases:

UDC: 513.881+517.53
MSC: 30A98, 46E15, 46B15

Citation: S. V. Bochkarev, “Existence of a basis in the space of functions analytic in the disk, and some properties of Franklin's system”, Mat. Sb. (N.S.), 95(137):1(9) (1974), 3–18; Math. USSR-Sb., 24:1 (1974), 1–16

Citation in format AMSBIB
\Bibitem{Boc74} \by S.~V.~Bochkarev \paper Existence of a~basis in the space of functions analytic in the disk, and some properties of Franklin's system \jour Mat. Sb. (N.S.) \yr 1974 \vol 95(137) \issue 1(9) \pages 3--18 \mathnet{http://mi.mathnet.ru/msb3738} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=355562} \zmath{https://zbmath.org/?q=an:0343.46016} \transl \jour Math. USSR-Sb. \yr 1974 \vol 24 \issue 1 \pages 1--16 \crossref{https://doi.org/10.1070/SM1974v024n01ABEH001732} 

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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. J. Bourgain, “New Banach space properties of the disc algebra and $H^{\infty}$”, Acta Math., 152:1 (1984), 1
2. A. V. Maslov, “On the Fourier coefficients with respect to the Haar system of functions in $L_p$-spaces”, Math. USSR-Sb., 54:2 (1986), 475–498
3. G. E. Tkebuchava, “On unconditional convergence with respect to systems of products of bases”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 231–244
4. G. G. Gevorkyan, “Majorants and uniqueness of series in the Franklin system”, Math. Notes, 59:4 (1996), 373–391
5. L. Gianone, J. Bokor, F. Schipp, “Approximate $\mathscr H_\infty$ identification using partial sum operators in a disc algebra basis”, IEEE Trans. Automat. Control, 43:8 (1998), 1117–1122
6. Yu. N. Subbotin, N. I. Chernykh, “Wavelets in spaces of harmonic functions”, Izv. Math., 64:1 (2000), 143–171
7. Hüseyin Akçay, “On the existence of a disk algebra basis”, Signal Processing, 80:5 (2000), 903
8. Holger Boche, Volker Pohl, “On the behavior of disk algebra bases with applications”, Signal Processing, 86:12 (2006), 3915
9. Holger Boche, Volker Pohl, “On the behavior of causal projections with applications”, Signal Processing, 87:12 (2007), 3108
10. G. E. Tkebuchava, K. Finet, “Unconditional Convergence of Fourier Expansions in Systems of Product Bases in Orlicz Spaces”, Math. Notes, 83:5 (2008), 675–683
11. G. G. Gevorgyan, A. S. Martirosyan, “Majorant and Paley function for series in general Franklin systems”, Proc. Steklov Inst. Math., 280 (2013), 132–143
12. Dubosarskii G.A., “Analiticheskie vspleski v oblasti s krugovymi granitsami”, Doklady akademii nauk, 448:4 (2013), 384–384
13. G. A. Dubosarskij, “Analytic Wavelets in Multiply Connected Domains with Circular Boundaries”, Math. Notes, 95:3 (2014), 359–373
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