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Quantitative extensions of the uniform boundedness principle. (English) Zbl 0634.41027
During the past decade the authors have developed a functional analytic approach to the problem of the sharpness of the various concrete error bounds arising in approximation theory and numerical analysis. See the monograph of the first two authors [Quantitative Prinzipien gleichmäßiger Beschränktheit und Schärfe von Fehlerabschätzungen, Forchungsber. Landes Nordrhein-Westfalen 3117, 110 S. (1982; Zbl 0493.41045)]. The purpose of this paper is to survey recent results in the subject.
Reviewer: H.R.Dowson

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A25 Rate of convergence, degree of approximation
41-02 Research exposition (monographs, survey articles) pertaining to approximations and expansions
42A45 Multipliers in one variable harmonic analysis
42A10 Trigonometric approximation
41A55 Approximate quadratures
41A05 Interpolation in approximation theory
Keywords:
error bounds
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