Bernstein type inequalities for splines

V.F. Babenko; V.A. Zontov

doi:10.15421/241203

Bernstein type inequalities for splines

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
V.A. Zontov (Oles Honchar Dnipropetrovsk National University)

Abstract

New sharp Bernstein type inequalities in the space $$$L_2(\mathbb{R})$$$ for the differences of non-periodic splines of order $$$m$$$ and minimal defect, having equidistant nodes, are obtained.

Keywords

non-periodic splines; B-splines; inequalities of Bernstein type

Full Text:

PDF (Русский)

References

Korneichuk N.P. Exact constants in approximation theory, Nauka, Moscow, 1987; 424 p. (in Russian)

Tikhomirov V.M. "Set widths in functional spaces and theory of the best approximations", Uspekhi mat. nauk, 1960; 15(3): pp. 81-120. (in Russian)

Subbotin Yu.N. "On the piecewise-polynomial interpolation", Mat. zametki, 1967; 1(1): pp. 24-29. (in Russian) doi:10.1007/BF01221723

Babenko V.F., Pichugov S.A. "Bernstein type inequalities for polynomial splines in $$$L_2$$$ space", Ukrainian Math. J., 1991; 43(3): pp. 420-422. (in Russian) doi:10.1007/BF01670081

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, Kyiv, 1992; 304 p. (in Russian)

Magaril-Il'yaev G.G. "On the best approximation of functional classes by splines on the real domain", Trudy Matematicheskogo instituta RAN, 1992; 194: pp. 148-159. (in Russian)

Babenko V.F., Zontov V.A. "Inequalities of Bernstein type for splines defined on the real domain", Ukrainian Math. J., 2011; 63(5): pp. 603-611. (in Russian) doi:10.1007/s11253-011-0536-6

Babenko V.F., Spektor S.A. "Inequalities of Bernstein type for splines in $$$L_2(\mathbb{R})$$$ space", Res. Math., 2008; 16(6/1): pp. 21-27. (in Russian)

Chui K. Introduction to wavelets, Moscow, 2008. (in Russian)