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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

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

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    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).

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

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

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

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

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

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

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

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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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Keywords

  • Unit Circle
  • Unit Disk
  • Carleman Approximation