Estimates of approximation of elements of Hilbert space by subspaces spanned by given unit expansion

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

Abstract


The exact inequalities of the Jackson-Chernih type of the approximation in the Hilbert space are obtained.

Keywords


best approximation; exact inequalities; Hilbert space; expansion unit; group unitary operators

References


Jackson D. Über die Genauigkeit der Annäherung stetiger Funktionen durch ganze rationale Funktionen gegebenen Grades und trigonometrische Summen gegebener Ordnung: Diss., Gottingen, 1911. (in German)

Akhiezer N.I., Glazman I.M. Theory of linear operators in Hilbert space, Moscow, 1966; 544 p. (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)

Horbachuk M.L., Hrushka Ya.I., Torba S.M. "Direct and Inverse Theorems in the Theory of Approximation by the Ritz Method", Ukrainian Math. J., 2005; 57(5): pp. 633-643. (in Ukrainian) doi:10.1007/s11253-005-0225-4

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)

Korneichuk N.P. "Exact constant in Jackson theorem of the best uniform appproximation of continuous periodic functions", Dokl. AN SSSR, 1962; 145: pp. 514-515. (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)

Torba S.M. Operator approach to direct and inverse theorems of approximation theory: Autoref. diss. for cand.phys.-math.sc., 2007. (in Ukrainian)

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




DOI: https://doi.org/10.15421/241006

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2010 V.F. Babenko, S.V. Savela

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


Registered in

More►


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