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Multivariate Approximation and Splines pp 1–12Cite as

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Multivariate Inequalities of Kolmogorov Type and Their Applications

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Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 125))

Abstract

Connections of inequalities of Kolmogorov type given in the form of inequalities for support functions of convex sets with some problems of analysis will be investigated. Our results will be oriented to applications in multivariate approximation. Exact inequalities which estimate L2-norms of derivatives of a multivariate periodic function with the help of L∞-norms of this function and its partial derivatives (of higher order) as well as analogues inequalities for primitives will be proved. Some results on approximation of classes of multivariate periodic functions by other classes which are obtained with the help of inequalities for primitives as well as some results on approximation of function classes by quasipolynomials will be presented.

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Author information

Authors and Affiliations

  1. Dnepropetrovsk State University, Pr. Gagarina, 72, Dnepropetrovsk, 320625, Ukraine

    V. F. Babenko, V. A. Kofanov & S. A. Pichugov

Authors
  1. V. F. Babenko
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  2. V. A. Kofanov
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  3. S. A. Pichugov
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131, Mannheim, Germany

    Günther Nürnberger  & Guido Walz  & 

  2. Institut für Numerische Mathematik, Technische Universität Dresden, D-01062, Dresden, Germany

    Jochen W. Schmidt

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© 1997 Springer Basel AG

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Babenko, V.F., Kofanov, V.A., Pichugov, S.A. (1997). Multivariate Inequalities of Kolmogorov Type and Their Applications. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds) Multivariate Approximation and Splines. ISNM International Series of Numerical Mathematics, vol 125. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8871-4_1

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  • DOI: https://doi.org/10.1007/978-3-0348-8871-4_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9808-9

  • Online ISBN: 978-3-0348-8871-4

  • eBook Packages: Springer Book Archive

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