Bernstein type inequalities of different metrics for splines defined on the real domain
Abstract
Keywords
Full Text:
PDF (Русский)References
Korneichuk N.P. Exact constants in approximation theory, Nauka, 1987.
Tikhomirov V.M. "Set widths in functional spaces and theory of the best approximations", Uspekhi matem. nauk, 1960; 15(3): pp. 81-120.
Subbotin Yu.N. "On the piecewise-polynomial interpolation", Matem. zametki, 1967; 1(1): pp. 24-29.
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.
Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, 1992.
Ligun A.A. "Sharp inequalities for spline-functions and the best quadrature formulas for certain classes of functions", Matem. zametki, 1976; 19(6): pp. 913-926.
Ligun A.A. "On inequalities between norms of derivatives of periodic functions", Matem. zametki, 1983; 33(3): pp. 385-391.
Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, 2003.
Kofanov V.A. "On sharp inequalities of Bernstein type for splines", Ukrainian Math. J., 2006; 58(10): pp. 1357-1367.
Magaril-Il'yaev G.G. "On the best approximation of functional classes by splines on the real domain", Trudy matem. inst. rAN, 1992; 194: pp. 148-159.
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.
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.
Hermander L. Linear differential operators with partial derivatives, Mir, 1965; 380 p.
Volevich L.R., Paneyakh B.P. "Certain spaces of generalized functions and inclusion theorems", Uspekhi matem. nauk, 1965; 20(1): pp. 3-74.
Mikhajlets V.A., Murach A.A. Hermander spaces, interpolation and elliptic problems, 2010; 372 p.
Strelkov N.A. "Projectively-net widths and lattice packings", Matem. sbor., 1991; 182(10): pp. 1513-1533.
Strelkov N.A. "Universally optimal wavelets", Matem. sbor., 1997; 188(1): pp. 147-160.
Chui K. Introduction to wavelets, Mir, 2008.
DOI: https://doi.org/10.15421/241303
Refbacks
- There are currently no refbacks.
Copyright (c) 2013 V.F. Babenko, V.A. Zontov

This work is licensed under a Creative Commons Attribution 4.0 International License.











