Geodesic
Approximation of Functions in Symmetrical and Connected Holder Spaces by Linear Means of Fourier–Vilenkin Series
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 287-294 
T. V. Likhacheva. Approximation of Functions in Symmetrical and Connected Holder Spaces by Linear Means of Fourier–Vilenkin Series. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 287-294. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a6/
@article{ISU_2014_14_3_a6,
     author = {T. V. Likhacheva},
     title = {Approximation of {Functions} in {Symmetrical} and {Connected} {Holder} {Spaces} by {Linear} {Means} of {Fourier{\textendash}Vilenkin} {Series}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {287--294},
     year = {2014},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a6/}
}
TY  - JOUR
AU  - T. V. Likhacheva
TI  - Approximation of Functions in Symmetrical and Connected Holder Spaces by Linear Means of Fourier–Vilenkin Series
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 287
EP  - 294
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a6/
LA  - ru
ID  - ISU_2014_14_3_a6
ER  - 
%0 Journal Article
%A T. V. Likhacheva
%T Approximation of Functions in Symmetrical and Connected Holder Spaces by Linear Means of Fourier–Vilenkin Series
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 287-294
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a6/
%G ru
%F ISU_2014_14_3_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper some summation methods are applied to Fourier-Vilenkin series in so called symmetric spaces. These methods use triangular matrix with sums in rows tending to zero and with some conditions on difference of coefficients. The triginometric counterpart of our results are due to M. L. Mittal, B. E. Rhoades, A. Guven, etc.

[1] Golubov B., Efimov A., Skvortsov V., Walsh series and transforms, Kluwer Academic Publishers, Dodrecht–Boston–London, 1991, 368 pp. | MR | MR | Zbl | Zbl

[2] Krein S., Petunin J., Semenov E., Interpolation of linear operators, Translations Math. Monographs, 55, Amer. Math. Soc., Providence, R.I., 1992 | MR | Zbl

[3] Volosivets S. S., “On Hardy and Bellman transforms of series with respect to multiplicative systems in symmetric spaces”, Analysis Math., 35:2 (2009), 131–148 | DOI | MR | Zbl

[4] Mittal M. L., Rhoades B. E., Mishra V. N., Singh V., “Using infinite matrix to approximate functions of class $Lip(\alpha,p)$ using trigonometric polynomials”, J. Math. Anal. Appl., 326:1 (2007), 667–676 | DOI | MR | Zbl

[5] Guven A., “Trigonometric approximation in reflexive Orlicz spaces”, Anal. Theory Appl., 27:2 (2011), 125–137 | DOI | MR | Zbl

[6] Iofina T. V., Volosivets S. S., “On the degree of approximation by means of Fourier–Vilenkin series in Holder and $L^p$ norm”, East J. Approximations, 15:2 (2009), 143–158 | MR

[7] Leindler L., “On the degree of approximation of continuous functions”, Acta Math. Hungar., 104 (2004), 105–113 | DOI | MR | Zbl

[8] Bari N. K., Stechkin S. B., “Best approximations and differential properties of two conjugate functions”, Trudy Mosk. mat. obshchestva, 5, 1956, 488–522 (in Russian)

[9] Lindenstrauss J., Tzafriri L., Classical Banach spaces, v. II, Springer, Berlin, 1973, 243 pp. | MR | Zbl

[10] Schipp F., “On $L^p$-norm convergence of series with respect to product systems”, Anal. Math., 2 (1976), 49–64 | DOI | MR | Zbl

[11] Simon S., “Verallgemeinerte Walsch–Fourierreihen”, Acta Math. Hungar., 27:3–4 (1976), 329–341 | DOI | MR | Zbl

[12] Hardy G. H., Divergent Series, Oxford Univ. Press, New York, 1949, 395 pp. | MR | Zbl

[13] Zelin H., “The derivatives and integrals of fractional order in Walsh–Fourier analysis with application to approximation theory”, J. Approx. Theory, 39:3 (1983), 261–273 | MR

[14] Fridli S., “On the rate of convergence of Cesaro means of Walsh–Fourier series”, J. Approx. Theory, 76:1 (1994), 31–53 | DOI | MR | Zbl