Approximation of certain classes of periodic functions with many variables

Ryozi SAKAI

doi:10.2969/jmsj/03310051

Ryozi SAKAI

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 1 Pages 51-65

DOI https://doi.org/10.2969/jmsj/03310051

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Published: 1981 Received: August 23, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Favard, Sur les meilleures procédés d'approximation de certaines classes des fonctions par des polynômes trigonométriques, Bull. sci. Math., 61 (1937), 209-224, 243-256.
2) N. I. Akhiezer and M. G. Krein, On the best approximation of periodic functions, Dokl. Akad. Nauk SSSR, 15 (1937).
3) N. I. Akhiezer, Über die Functionen die in gegebenen Intervallen am wenigsten von Null abweichen, Izv. Kaz. fiz. mat. ob-va, 3 (1928).
4) N. I. Akhiezer, Theory of approximation, Ungar, New York; Constable, London, 1956.
5) N. P. Korneicuk, Upper bounds of best approximations on classes of differentiable periodic functions in the C and L metrics, Dokl. Akad. Nauk SSSR, 190 (1970), 77-80=Soviet Math. Dokl., 11 (1970).
6) B. Sz. Nagy, Über gewisse Extremalfragen bei transformierten trigonometrischen Entwicklungen, Berichte Akad. Wiss. Leipzig, 90 (1938).
7) A. F. Timan, Theory of approximation of functions of a real variable, Macmillan, New York, 1963.
8) G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, 1966.

Right : [1] J. Favard, Sur les meilleures procédés d'approximation de certaines classes des fonctions par des polynômes trigonométriques, Bull. sci. Math., 61 (1937), 209-224, 243-256.
[2] N. I. Akhiezer and M. G. Krein, On the best approximation of periodic functions, Dokl. Akad. Nauk SSSR, 15 (1937).
[3] N. I. Akhiezer, Über die Functionen die in gegebenen Intervallen am wenigsten von Null abweichen, Izv. Kaz. fiz. mat. ob-va, 3 (1928).
[4] N. I. Akhiezer, Theory of approximation, Ungar, New York; Constable, London, 1956.
[5] N. P. Korneicuk, Upper bounds of best approximations on classes of differentiable periodic functions in the C and L metrics, Dokl. Akad. Nauk SSSR, 190 (1970), 77-80=Soviet Math. Dokl., 11 (1970).
[6] B. Sz. Nagy, Über gewisse Extremalfragen bei transformierten trigonometrischen Entwicklungen, Berichte Akad. Wiss. Leipzig, 90 (1938).
[7] A. F. Timan, Theory of approximation of functions of a real variable, Macmillan, New York, 1963.
[8] G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, 1966.

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