×

zbMATH — the first resource for mathematics

Approximation of functions of several variables by de la Vallee Poussin rectangular sums. (English. Russian original) Zbl 0491.42002
Math. Notes 29, 362-372 (1981); translation from Mat. Zametki 29, 711-730 (1981).
MSC:
42A10 Trigonometric approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
41A25 Rate of convergence, degree of approximation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] H. Lebesgue, ?Sur la représentation trigonométrique approchée des fonction satisfaisant a une condition de Lipschitz,? Bull. Soc. Math. France,38, 184-210 (1910). · JFM 41.0476.02
[2] Ch. de La Vallée Poussin, Lecons sur l’Approximation des Fonctions d’une Variable Réelle, Paris (1919). · JFM 47.0908.02
[3] S. M. Nikol’skii, ?On certain methods of approximation by trigonometric sums,? Izv. Akad. Nauk SSSR, Ser. Mat.,4, 509-520 (1940).
[4] S. B. Stechkin, ?On the approximation of periodic functions by Fejér sums,? Tr. Mat. Inst. Akad. Nauk SSSR,62, 48-60 (1961).
[5] K. I. Oskolkov, ?On the Lebesgue inequality in the uniform metric and on a set of full measure,? Mat. Zametki,18, No. 4, 515-526 (1975). · Zbl 0339.42001
[6] K. I. Oskolkov, ?On the Lebesgue inequality in the mean,? Mat. Zametki,25, No. 4, 551-555 (1979). · Zbl 0414.42002
[7] S. B. Stechkin [S. B. Ste?kin], ?On the approximation of a periodic function by de la Vallée Poussin sums,? Anal. Math.,4, 61-74 (1978). · Zbl 0393.41009 · doi:10.1007/BF01904859
[8] W. Dahmen, ?On the best approximation and de la Vallée Poussin sums,? Mat. Zametki,23, No. 5, 671-686 (1978).
[9] S. P. Baiborodov, ?Approximation of functions by de la Vallée Poussin sums,? Mat. Zametki,27, No. 1, 33-48 (1980).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.