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Some Recent Applications of Functional Analysis to Approximation Theory

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Book cover Zum Werk Leonhard Eulers

Abstract

A major portion of approximation theory is concerned with the approximation of functions by polynomials or by sequences {Tn} of linear operators, more specifically with the connections between the structural properties of the function f being approximated and the convergence per se and/or rate of convergence of ‖Tn (f) — f ‖ to zero for n → ∞. in particular, the wide area of approximation theory and its applications is devoted to the convergence per se and the rate of vonvergence of, for example, (a) the best trigonometric approximation of a given function, (b) the partial sums of the Fourier series of a function to the function. itself, (c) the solution of Dirichlet’s problem for the unit disk to the given boundary value, (d) the Whittaker — Shannon sampling series expansion of a duration-limited function to the functioninquestion, (e) the sums occuring in the weak law of large numbers in probability theory.

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Authors and Affiliations

  1. Lehrstuhl A für Mathematik, Rheinisch-Westfälische Technische Hochschule Aachen, D 5100, Aachen, Federal Republic of Germany

    P. L. Butzer

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  1. P. L. Butzer
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Editors and Affiliations

  1. Institut für Philosophie, Wissenschaftstheorie, Wissenschafts- und Technikgeschichte, Technische Universität Berlin, Straße des 17. Juni 135, D 1000, Berlin 12, Deutschland

    Eberhard Knobloch

  2. Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2-6, D 1000, Berlin 33, Deutschland

    Ilppo Simo Louhivaara

  3. Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 135, D 1000, Berlin 12, Deutschland

    Jörg Winkler

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© 1984 Birkhäuser Verlag Basel

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Butzer, P.L. (1984). Some Recent Applications of Functional Analysis to Approximation Theory. In: Knobloch, E., Louhivaara, I.S., Winkler, J. (eds) Zum Werk Leonhard Eulers. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7121-1_7

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  • DOI: https://doi.org/10.1007/978-3-0348-7121-1_7

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7122-8

  • Online ISBN: 978-3-0348-7121-1

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