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

This article is cited in 13 scientific papers (total in 13 papers)

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
Received: 20.05.1974

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
\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
\jour Math. USSR-Sb.
\yr 1974
\vol 24
\issue 1
\pages 1--16

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    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  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. G. G. Gevorkyan, “Majorants and uniqueness of series in the Franklin system”, Math. Notes, 59:4 (1996), 373–391  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath
    6. Yu. N. Subbotin, N. I. Chernykh, “Wavelets in spaces of harmonic functions”, Izv. Math., 64:1 (2000), 143–171  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Hüseyin Akçay, “On the existence of a disk algebra basis”, Signal Processing, 80:5 (2000), 903  crossref
    8. Holger Boche, Volker Pohl, “On the behavior of disk algebra bases with applications”, Signal Processing, 86:12 (2006), 3915  crossref
    9. Holger Boche, Volker Pohl, “On the behavior of causal projections with applications”, Signal Processing, 87:12 (2007), 3108  crossref
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. Dubosarskii G.A., “Analiticheskie vspleski v oblasti s krugovymi granitsami”, Doklady akademii nauk, 448:4 (2013), 384–384  elib
    13. G. A. Dubosarskij, “Analytic Wavelets in Multiply Connected Domains with Circular Boundaries”, Math. Notes, 95:3 (2014), 359–373  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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