Best approximation and K-functionals

Acta Mathematica Hungarica

Volumn 75, Issue 3, 1997, Pages 165-208

  Chen, W ^a   Ditzian, Z ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031285766     PISSN: 02365294     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006543020828     Document Type: Article

References (19)

1. R. Askey and I. J. Hirschman, Mean summability for ultraspherical polynomials, Math. Scand., 12 (1963), 167-177.
2. R. Askey and S. Wainger, A convolution structure for Jacobi series, Amer. J. Math., 91 (1969), 463-485.
3. A. Bonami and J. L. Clerc, Sommes de Cesàro et multiplicateurs des developpements en harmoniques sphériques, Trans. Amer. Math. Soc., 183 (1973), 223-263.
4. J. Czipszer and G. Freud, Sur l'approximation d'une fonction périodique et de ses dérivées successives par un polynome trigonométrique at par ses dérivées successives, Acta Math., 99 (1958), 33-51.
5. Z. Ditzian, A measure of smoothness related to the Laplacian, Trans Amer. Math. Soc., 326 (1991), 407-422.
6. Z. Ditzian, A K-functional and the rate of convergence of some linear polynomial operators, Proc. Amer. Math. Soc., 124 (1996), 1773-1781.
7. Z. Ditzian and K. Ivanov, Strong converse inequalities, Jour. d'Analyse Math., 61 (1993), 61-111.
8. p, 0 < p < 1, Constructive Approximation, 11 (1995), 67-83.
9. Z. Ditzian and V. Totik, Moduli of Smoothness, Springer-Verlag (1987).
10. V. H. Hristov and K. Ivanov, Realization of K-functionals on subsets and constrained approximation, Math. Balkanica, 4 (new series), (1990), 236-257.
11. Hardy, Divergent Series, Oxford University Press (1949).
12. G. Gasper, Banach algebras for Jacobi series and positivity of a kernel, Annals of Math., 95 (1972), 261-280.
13. E. Görlich and C. Markett, On approximation by Cesàro means of Laguerre expansion and best approximation, Resultate der Mathematik, 2 (1979), 124-150.
14. D. Lubinsky and V. Totik, Best weighted polynomial approximation via Jacobi expansions, SIAM J. of Math. Anal., 28 (1994), 555-570.
15. p metric, Soviet Math. Dokl, 34 (1987), No. 1.
16. E. L. Poiani, Mean Cesàro summability of Laguerre and Hermite series, Trans. Amer. Math. Soc., 173 (1972), 1-31.
17. E. M. Stein, Localization and summability of multiple Fourier series, Acta Math., 100 (1958), 93-146.
18. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press (1971).
19. G. Szego, Orthogonal Polynomials, American Math. Soc. Coll. Publ. Vol. 23 (1959).