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Dahmen, W.; Görlich, E.

Best approximation with exponential orders and intermediate spaces. (English) Zbl 0318.41022

Math. Z. 148, 7-21 (1976).
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scan of Zbl 0318.41022

Cited in 2 Reviews
Cited in 6 Documents

MSC:

41A50 Best approximation, Chebyshev systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
26D15 Inequalities for sums, series and integrals
41A25 Rate of convergence, degree of approximation
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Full Text: DOI EuDML

References:

[1] Butzer, P. L., Berens, H.: Semi-Groups of Operators and Approximation. Berlin-Heidelberg-New York: Springer 1967 · Zbl 0164.43702
[2] Butzer, P. L., Scherer, K.: On the fundamental approximation theorems of D. Jackson, S. N. Bernstein and Theorems of M. Zamansky and S. B. Ste?kin. Aequationes math.3, 170-185 (1969) · Zbl 0179.09101 · doi:10.1007/BF01817511
[3] Butzer, P. L., Scherer, K.: Über die Fundamentalsätze der klassischen Approximationstheorie in abstrakten Räumen. In: Abstract Spaces and Approximation (ed. by P. L. Butzer and B. Sz.-Nagy) ISNM vol. 10, pp. 113-125. Basel: Birkhäuser 1969 · Zbl 0186.11001
[4] Dahmen, W., Görlich, E.: A conjecture of Golomb on optimal and nearly-optimal linear approximation. Bull. Amer. math. Soc.80, 1199-1202 (1974) · Zbl 0294.41019 · doi:10.1090/S0002-9904-1974-13676-1
[5] Dahmen, W., Görlich E.: Asymptotically optimal linear approximation processes and a conjecture of Golomb. In: Linear Operators and Approximation II (ed. by P. L. Butzer and B. Sz.-Nagy) ISNM vol. 25, pp. 327-335. Basel: Birkhäuser 1974 · Zbl 0303.41015
[6] du Bois-Reymond, P.: Sur la grandeur relative des infinis des fonctions. Ann. Mat. pura appl., II. Ser.4, 338-353 (1871) · JFM 03.0197.01
[7] du Bois-Reymond, P.: Théorème général concernant la grandeur relative des infinis des fonctions et de leurs dérivées. J. reine angew. Math.74, 294-304 (1872) · JFM 04.0196.01
[8] Görlich, E., Nessel, R. J., Trebels, W.: Bernstein-type inequalities for families of multiplier operators in Banach spaces with Cesàro decompositions. I. General theory, II. Applications. Acta Sci. math.34, 121-130 (1973);36, 39-48 (1974) · Zbl 0269.42007
[9] Hardy, G. H.: Orders of infinity. Cambridge: Cambridge University Press 1954 · Zbl 0058.03301
[10] Johnen, H.: Inequalities connected with the moduli of smoothness. Mat. Vesnik, n. Ser.9 (24), 289-303 (1972) · Zbl 0254.26005
[11] Junggeburth, J., Scherer, K., Trebels, W.: Zur besten Approximation auf Banachräumen mit Anwendungen auf ganze Funktionen. Forschungsberichte des Landes Nordrhein-Westfalen Nr. 2311, Opladen: Westdeutscher Verlag 1973 · Zbl 0267.41011
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