Inequality of Taikov type for powers of normal operators in Hilbert space

V.F. Babenko; R.O. Bilichenko

doi:10.15421/241101

Inequality of Taikov type for powers of normal operators in Hilbert space

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

Abstract

The Taikov inequality, which estimates $$$L_{\infty}$$$-norm of intermediate derivative by $$$L_2$$$-norms of a function and its higher derivative, is extended on arbitrary powers of normal operator acting in Hilbert space.

Keywords

normal operator; spectral theorem; Hilbert space

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References

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

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