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

V.F. Babenko; S.V. Savela

doi:10.15421/241006

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

Full Text:

PDF (Русский)

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)

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

Torba S.M. Operator approach to direct and inverse theorems of approximation theory: Autoref. Diss. Cand. Phys.-Math. Sc., 2007. (in Ukrainian)

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

Akhiezer N.I., Glazman I.M. Theory of linear operators in Hilbert space, Nauka, 1966.

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.

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.

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.

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

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