Integral presentations of deviations of de la Vallee Poussin right-angled sums

Vladimir I. Rukasov; Olga G. Rovenska

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2009)

  • Volume: 48, Issue: 1, page 129-137
  • ISSN: 0231-9721

Abstract

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We investigate approximation properties of de la Vallee Poussin right-angled sums on the classes of periodic functions of several variables with a high smoothness. We obtain integral presentations of deviations of de la Vallee Poussin sums on the classes C β , m α .

How to cite

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Rukasov, Vladimir I., and Rovenska, Olga G.. "Integral presentations of deviations of de la Vallee Poussin right-angled sums." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 48.1 (2009): 129-137. <http://eudml.org/doc/35178>.

@article{Rukasov2009,
abstract = {We investigate approximation properties of de la Vallee Poussin right-angled sums on the classes of periodic functions of several variables with a high smoothness. We obtain integral presentations of deviations of de la Vallee Poussin sums on the classes $C_\{\beta ,\infty \}^\{m\alpha \}$.},
author = {Rukasov, Vladimir I., Rovenska, Olga G.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Right-angled sums of Vallee Poussin; integral presentations; Fourier series; right-angled sums of Vallee Poussin; integral representations; Fourier series},
language = {eng},
number = {1},
pages = {129-137},
publisher = {Palacký University Olomouc},
title = {Integral presentations of deviations of de la Vallee Poussin right-angled sums},
url = {http://eudml.org/doc/35178},
volume = {48},
year = {2009},
}

TY - JOUR
AU - Rukasov, Vladimir I.
AU - Rovenska, Olga G.
TI - Integral presentations of deviations of de la Vallee Poussin right-angled sums
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2009
PB - Palacký University Olomouc
VL - 48
IS - 1
SP - 129
EP - 137
AB - We investigate approximation properties of de la Vallee Poussin right-angled sums on the classes of periodic functions of several variables with a high smoothness. We obtain integral presentations of deviations of de la Vallee Poussin sums on the classes $C_{\beta ,\infty }^{m\alpha }$.
LA - eng
KW - Right-angled sums of Vallee Poussin; integral presentations; Fourier series; right-angled sums of Vallee Poussin; integral representations; Fourier series
UR - http://eudml.org/doc/35178
ER -

References

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  2. Lassuria, R. A., Multiple Fourier sums on the sets of ψ ¯ -differentiable functions, Ukrainian Math. J. 55, 7 (2003), 911–918 (in Russian). (2003) MR2073861
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  9. Rukasov, V. I., Chaichenko, S. O., Approximation of the classes of analytical functions by de la Vallee-Poussin sums, Ukrainian Math. J. 55, 6 (2003), 575–590. (2003) MR2071790
  10. Rukasov, V. I., Chaichenko, S. O., Approximation of continuous functions by de la Vallee-Poussin operators, Ukrainian Math. J. 55, 3 (2003), 498–511. (2003) MR2071386
  11. Rukasov, V. I., Novikov, O. A., Approximation of analytical functions by de la Vallee Poussin sums. Fourier series: Theory and Applications, Works of the Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, 1998, 228–241 (in Russian). (1998) MR1762839
  12. Stepanec A. I., Rukasov V. I., Chaichehko S. O., Approximation by de la Vallee Poussin sums, Works of the Institute of Mathematics, Ukrainian Academy of Sciences, 68, 2007, 368 pp. (in Russian). (2007) 
  13. Rukasov, V. R., Novikov, O. A., Velichko, V. E., Rovenska, O. G., Bodraya, V. I., Approximation of the periodic functions of many variables with a high smoothness by Fourier right-angled sums, Works of the Institute of Mathematics and Mechanics, Ukrainian Academy of Sciences, 2008, 163–170 (in Russian). (2008) MR2536626
  14. Rukasov, V. I., Novikov, O. A., Bodraya, V. I., Approximation of the classes of functions of two variables with a high smoothness by the right-angled linear means of Fourier series. Problems of the aproximation of the functions theory and closely related concepts, Works of the Institute of Mathematics, Ukrainian Academy of Sciences, 4, 1 (2007), 270–283 (in Russian). (2007) 
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