Uniqueness of Best L1-Approximations of Continuous Functions

  • Manfred Sommer
Chapter
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 74)

Abstract

The problem of uniqueness of best approximations of continuous vector-valued functions and continuous functions of one and several variables by finite dimensional subspaces in the weighted L1-norm is studied. Characterizations of uniqueness of best approximations are obtained. Various examples of subspaces which guarantee uniqueness, including subspaces of polynomials and linear spline functions of two variables, are presented.

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Copyright information

© Birkhäuser Verlag Basel 1985

Authors and Affiliations

  • Manfred Sommer
    • 1
  1. 1.Mathematisch-Geographische FakultätKatholische Universität EichstättEichstättFederal Republik of Germany

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