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Nikolskiĭ Constants for Positive Singular Integrals of Perturbed Fejér-Type

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Linear Operators and Approximation / Lineare Operatoren und Approximation

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Abstract

Concerning the approximation of periodic functions by means of positive singular integrals, the problem of determining the best asymptotic or Nikolskiĭ constant for the measure of approximation with respect to Lipschitz classes was solved in general provided the corresponding kernel is of Fejér’s type. But there is still a number of important examples to which this theory does not apply. It is shown that for kernels of perturbed Fejér-type the associate Nikolskiĭ constant may be evaluated by a simple comparison theorem.

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Authors and Affiliations

  1. Lehrstuhl a für Mathematik, Technische Hochschule Aachen, Germany

    Eberhard L. Stark

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Editors and Affiliations

  1. Aachen, Germany

    P. L. Butzer

  2. Paris, France

    J.-P. Kahane

  3. Szeged, Hungary

    B. Szökefalvi-Nagy

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© 1972 Birkhäuser Verlag Basel

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Stark, E.L. (1972). Nikolskiĭ Constants for Positive Singular Integrals of Perturbed Fejér-Type. In: Butzer, P.L., Kahane, JP., Szökefalvi-Nagy, B. (eds) Linear Operators and Approximation / Lineare Operatoren und Approximation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7283-6_31

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  • DOI: https://doi.org/10.1007/978-3-0348-7283-6_31

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7285-0

  • Online ISBN: 978-3-0348-7283-6

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