References
K. Runovski and H.-J. Schmeisser, On Modulus of Continuity Related to Riesz Derivative, Preprint, Jenaer Schriften fÜrMath. und Inf.Math/Inf/01/11 (2011).
S. Yu. Artamonov, Uch. Zap. V. N. Vernadskii TNU, Ser.Matem.Mekh. Inform. i Kibernet. 24 (63) (3), 10 (2011).
Z. Burinska, K. Runovski, and H.-J. Schmeisser, Sampl. Theory Signal Image Process. 5 (1), 59 (2006).
L. Hörmander, The Analysis of Linear Partial Differential Operators. I: Distribution Theory and Fourier Analysis, in Grundlehren Math. Wiss. (Springer-Verlag, Berlin, 1983), vol. 256.
Z. Burinska, K. Runovski, and H.-J. Schmeisser, Sampl. Theory Signal Image Process. 8 (2), 105 (2009).
P. L. Butzer, W. Splettstösser, and R. Stens, Jahresber. Deutsch.Math.-Verein. 90 (1), 1 (1988).
N. I. Akhiezer, Lecture in the Theory of Approximation (Nauka, Moscow, 1965) [in Russian].
H.-J. Schmeisser and W. Sickel, in Applied Mathematics Reviews (World Sci., Singapore, 2000), Vol. 1, pp. 205–284.
K. Runovski and H.-J. Schmeisser, Eurasian Math. J. 2 (3), 98 (2011).
R. DeVore and G. Lorentz, Constructive Approximation, in Grundlehren Math. Wiss. (Springer-Verlag, Berlin, 1993), vol. 303.
H. Triebel, Theory of Function Spaces, in Mathematik und ihre Anwendungen in Physik und Technik (Akad. Verlag. Geest & Portig K.-G., Leipzig, 1983), vol. 38.
D. Jackson, Über die Genauigkeit der Annäherung stetiger Funktionen durch ganze rationale Funktionen gegebenen Grades und trigonometrischen Summen gegebener Ordnung, Diss. (Göttingen, 1911).
S. B. Stechkin, Izv. Akad. Nauk SSSR Ser. Mat. 15 (3), 219 (1951).
K. V. Runovskii, Mat. Zametki 95 (6), 899 (2014) [Math. Notes 95 (5–6), 833 (2014)].
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Original Russian Text © S. Yu. Artamonov, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 6, pp. 933–936.
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Artamonov, S.Y. Nonperiodic modulus of smoothness corresponding to the Riesz derivative. Math Notes 99, 928–931 (2016). https://doi.org/10.1134/S0001434616050321
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DOI: https://doi.org/10.1134/S0001434616050321