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Impossibility of the Carleman approximation of functions continuous on the unit circle by the boundary values of functions analytic and uniformly continuous on the unit disk

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Literature cited

  1. T. Carleman, “Sur un théoréme de Weierstrass,” Arkiv Math. Astron. Fis.,20, No. 4, 1–5 (1927).

    Google Scholar 

  2. N. U. Arakelyan, “On uniform and asymptotic approximation by entire functions on unbounded closed sets,” Dokl. Akad. Nauk SSSR,157, No. 1, 9–11 (1964).

    Google Scholar 

  3. K. Hoffman, Banach Spaces of Analytic Functions, (1962).

  4. A. Zygmund, Trigonometric Series, Vol. 1, Cambridge Univ. Press (1959).

  5. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Moscow-Leningrad (1950).

  6. L. V. Kantorovich and G. P. Akilov, Functional Analysis and Normed Spaces [in Russian], Moscow (1959).

  7. V. P. Khavin, “Spaces of analytic functions,” in: Progress in Mathematics, Vol. 1, Plenum Press, New York (1968), pp. 76–167.

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  8. M. Brelot, Elements of Classical Potential Theory [Russian translation], Moscow (1964).

  9. K. Hoffman, “Analytic functions and logmodular Banach algebras,” Acta Math.,108, 271–317 (1962).

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  10. I. Glicksberg and J. Wermer, “Measures orthogonal to a Dirichlet algebra,” Duke Math. J.,30, No. 4, 661–666 (1963).

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Authors
  1. V. P. Khavin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 22, pp. 161–170, 1971.

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Khavin, V.P. Impossibility of the Carleman approximation of functions continuous on the unit circle by the boundary values of functions analytic and uniformly continuous on the unit disk. J Math Sci 2, 193–200 (1974). https://doi.org/10.1007/BF01099676

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  • DOI: https://doi.org/10.1007/BF01099676

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