Approximation of unbounded functionals by the bounded ones in Hilbert space

V.F. Babenko (Oles Honchar Dnipropetrovsk National University),
R.O. Bilichenko (Oles Honchar Dnipropetrovsk National University)


We obtained the value of the best approximation of unbounded functional $$$F_f(x) = (A^kx, f)$$$ on the class $$$\{ x\in D(A^r) \colon \| A^r x \| \leqslant 1 \}$$$ by linear bounded functionals ($$$A$$$ is a self-adjoint operator in the Hilbert space $$$H$$$, $$$f\in H$$$, $$$k < r$$$).


functional; self-adjoint operator; Hilbert space


Arestov V.V., Gabushin V.N. "The best approximation of unbounded operators by the bounded ones", Izv. vuzov. Matematika, 1995; 11: pp. 42-63. (in Russian)

Arestov V.V. "Approximation of unbounded operators by the bounded ones and related extremum problems", Uspekhi mat. nauk, 1996; 51(6): pp. 88-124. (in Russian) doi:10.1070/RM1996v051n06ABEH003001

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

Babenko V.F., Bilichenko R.O. "Inequalities of Taikov type for self-adjoint operators in Hilbert space", Trudy IPMM, 2010; 21: pp. 11-18. (in Russian)

Berezanskij Yu.M., Us G.F., Sheftel' Z.G. Functional analysis, Kyiv, 1990; 600 p. (in Russian)

Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Nauk. dumka, Kyiv, 2003; 590 p. (in Russian)

Stechkin S.B. "Inequalities between norms of derivatives of arbitrary function", Acta scient. math., 1965; 26: pp. 225-230. (in Russian)

Stechkin S.B. "The best approximation of linear operators", Matem. zametki, 1967; 1(2): pp. 137-148. (in Russian) doi:10.1007/BF01268056

Taikov L.V. "Inequalities of Kolmogorov type and the best formulas of numeric differentiation", Matem. zametki, 1968; 4(2): pp. 223-238. (in Russian) doi:10.1007/BF01094964

Shadrin A.Yu. "Inequalities of Kolmogorov type and estimates of spline-interpolation for periodic classes $$$W^m_2$$$", Matem. zametki, 1990; 48(4): pp. 132-139. (in Russian) doi:10.1007/BF01139609




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