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Right-angled sums of Vallee Poussin; integral presentations; Fourier series

References:

[1] Stepanec, A. I., Pachulia, N. L.: **Multiple Fourier sums on the sets of $(\psi ,\beta )$-differentiable functions**. Ukrainian Math. J. 43, 4 (1991), 545–555 (in Russian). MR 1117897

[2] Lassuria, R. A.: **Multiple Fourier sums on the sets of $\overline{\psi }$-differentiable functions**. Ukrainian Math. J. 55, 7 (2003), 911–918 (in Russian). MR 2073861

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[8] Stepanec, A. I.: **Approximation by Fourier sums of de la Poussin integrals of continuous functions**. Lect. of Rus. Acad. of Sc. 373, 2 (2000), 171–173 (in Russian).

[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. MR 2071790

[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. MR 2071386

[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). MR 1762839

[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).

[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). MR 2536626

[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).

[15] Stepanec, A. I.: **Classification and approximation of periodic functions**. Nauk. Dumka, Kiev, 1987 (in Russian). MR 0918146