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

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


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.


normal operator; spectral theorem; Hilbert space


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




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ISSN (Online): 2664-5009
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