On the best $$$L_2$$$-approximations of multivariable functions by means of splines

V.F. Babenko (Dnipropetrovsk National University, Institute of Applied Mathematics and Mechanics of NAS of Ukraine), https://orcid.org/0000-0001-6677-1914
G.S. Zhiganova (Dnipropetrovsk National University)

Abstract


We obtain sharp inequalities of Jackson type for the best approximations of functions in $$$L_2(\mathbb{R}^m)$$$ by means of partial sums of wavelet series in case of multidimensional analogues of Shannon-Kotelnikov wavelets.

References


Babenko A.G. "Sharp Jackson-Stechkin inequality in space $$$L_2$$$ of functions on multidimensional sphere", Matem. zametki, 1996; 60(3): pp. 333-355. (in Russian) doi:10.1007/BF02320361

Ivanov V.I., Smirnov O.I. "Jackson and Young constants in $$$L_p$$$ spaces", Tula State Univ., 1995. (in Russian)

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

Ligun A.A. "Exact constants in inequalities of Jackson type", Special problems of approx. theory and optim. control of distrib. systems, Kyiv, 1990; pp. 5-74. (in Russian)

Chernykh N.I. "On Jackson inequality in $$$L_2$$$ space", Trudy MIAN SSSR, 1967; 88: pp. 71-74. (in Russian)

Chernykh N.I. "On the best approximation of periodic functions by trigonometrical polynomials in $$$L_2$$$", Matem. zametki, 1967; 2(5): pp. 513-522. (in Russian) doi:10.1007/BF01093942

Ibragimov I.I., Nasibov F.G. "On the estimation of the best approximation of summable function on the real domain by entire functions of finite degree", Dokl. AN SSSR, 1970; 194(5): pp. 1013-1016. (in Russian)

Popov V.Yu. "On the best mean-square approximations by entire functions of exponential type", Izv. vuzov. Matem., 1972; 121(6): pp. 65-73. (in Russian)

Yudin V.A. "Multidimensional Jackson's theorem in $$$L_2$$$", Matem. zametki, 1981; 29(2): pp. 309-315. (in Russian) doi:10.1007/BF01140931

Moskovskii A.V. "Jackson's theorems in $$$L_p(\mathbb{R}^n)$$$ and $$$L_{p,\lambda}(\mathbb{R}_+)$$$ spaces", Izv. Tulskogo gos. un-ta. Ser. matem., mekh., inform., 1997; 3(1): pp. 44-70. (in Russian)

Pichugov S.A. "On approximation of periodic multivariable functions in metric $$$L_2$$$", Res. on modern problems of summ. and approx. of functions and their applic., 1976; pp. 49-50. (in Russian)

Babenko V.F., Zhiganova G.S., Novikova L.S. "On inequalities of Jackson type for the best $$$L_2$$$-approximations by wavelets", Res. Math., 2006; 11: pp. 3-8. (in Russian)

Kashin V.S., Saakian A.A. Orthogonal series, 1999. (in Russian)

Strelkov N.A. "Universally optimal wavelets", Matem. sbornik, 1997; 188(1): pp. 147-160. (in Russian) doi:10.1070/SM1997v188n01ABEH000192




DOI: https://doi.org/10.15421/240701

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2007 V.F. Babenko, G.S. Zhiganova

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


Registered in


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU