Quantitative extensions of the uniform boundedness principle. (English) Zbl 0634.41027

Dickmeis, W.; Nessel, R. J.; van Wickeren, E.

Jahresber. Dtsch. Math.-Ver. 89, 105-134 (1987).

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

Citations:

Zbl 0493.41045