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On series with respect to the Faber-Schauder system and with respect to the bases of the space C[0, 1]

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Abstract

In this paper we investigate the sequence of coefficients of the expansions of continuous functions with respect to normed and quasinormed bases of the space C[0, 1]. In this connection one makes use in an essential way of the properties of the Faber-Schauder system of functions. Some adjoining questions are investigated.

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Literature cited

  1. P. L. Ul'yanov, “On series with respect to the Haar system,” Matem. Sb.,63, No. 3, 356–391 (1964).

    Google Scholar 

  2. G. Faber, “Über die Orthogonalfunktionen des Herrn Haar,” Jahresber. Deutsch. Math. verein.,19, 104–112 (1910).

    Google Scholar 

  3. J. Schauder, “Zur Theorie stetiger Abbildungen in Funktionalräumen,” Math. Zeitschr.,26, 47–65 (1927).

    Google Scholar 

  4. M. M. Day, Normed Linear Spaces, Springer, Berlin (1962).

    Google Scholar 

  5. M. A. Meletidi, “On the bases in the spaces C and Lp,” Matem. Zametki,10, No. 6, 635–640 (1971).

    Google Scholar 

  6. A. M. Olevskii, “On the divergence of orthogonal series and Fourier coefficients of continuous functions with respect to complete systems,” Sibirsk. Matem. Zh.,4, No. 3, 647–656 (1963).

    Google Scholar 

  7. A. M. Olevskii, “Fourier series of continuous functions with respect to bounded orthonormal systems,” Izv. Akad. Nauk SSSR, Ser. Matem.,30, No. 2, 387–432 (1966).

    Google Scholar 

  8. V. I. Gurarii and N. I. Gurarii, “On bases in uniformly convex and uniformly smooth Banach spaces,” Izv. Akad. Nauk SSSR, Ser. Matem.,35, No. 1, 210–215 (1970).

    Google Scholar 

  9. N. I. Gurarii, “On the sequences of the coefficients of expansions with respect to bases in Hilbert and Banach spaces,” Izv. Akad. Nauk SSSR, Ser. Mate.,35, No. 1, 216–223 (1970).

    Google Scholar 

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Authors and Affiliations

  1. Odessa State University, USSR

    V. G. Krotov

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  1. V. G. Krotov
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Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 185–195, August, 1973.

The author expresses his thanks to V. A. Andrienko for his constant interest in this paper.

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Krotov, V.G. On series with respect to the Faber-Schauder system and with respect to the bases of the space C[0, 1]. Mathematical Notes of the Academy of Sciences of the USSR 14, 665–670 (1973). https://doi.org/10.1007/BF01147110

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  • DOI: https://doi.org/10.1007/BF01147110

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