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Constructive properties of functions with variable smoothness

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Abstract

Analogs of theorems of Jensen and Weierstrass are proven for functions of variable smoothness, defined on the real line.

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Literature cited

  1. S. Bochner, “Localization of best approximation,” Ann. Math. Stud.,25, 3–23 (1950).

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  3. Yu. A. Brudnyi, “Approximation by entire functions on a real interval and on a half-line,” Dokl. Akad. Nauk SSSR,124, No. 4, 739–742 (1959).

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    V. Ya. Yanchak

Authors
  1. V. Ya. Yanchak
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Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 443–449, October, 1970.

In conclusion I wish to express my gratitude to S. M. Nikol'skii and S. B. Stechkin for their valuable advice concerning this work.

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Yanchak, V.Y. Constructive properties of functions with variable smoothness. Mathematical Notes of the Academy of Sciences of the USSR 8, 718–721 (1970). https://doi.org/10.1007/BF01104371

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