The best approximation of classes, defined by powers of self-adjoint operators acting in Hilbert space, by other classes

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 best approximation of class of elements such that $$$\| A^k x \| \leqslant 1$$$ by classes of elements such that $$$\| A^r x \| \leqslant N$$$, $$$N > 0$$$ for powers $$$k < r$$$ of self-adjoint operator $$$A$$$ in Hilbert space $$$H$$$ is found.

References


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

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)

Korneichuk N.P. "Inequalities for differentiable periodic functions and the best approximation of one class of functions by another", Izv. AN SSSR. Ser. Matem., 1972; 36(2): pp. 423-434. (in Russian) doi:10.1070/IM1972v006n02ABEH001880

Korneichuk N.P. Extremum problems in approximation theory, Moscow, 1976; 320 p. (in Russian)

Korneichuk N.P. "Extreme values of functionals and the best approximation on classes of periodic functions", Izv. AN SSSR. Ser. Matem., 1971; 35(1): pp. 93-124. (in Russian) doi:10.1070/IM1971v005n01ABEH001015

Subbotin Yu.N., Taikov L.V. "The best approximation of a differentiation operator in $$$L_2$$$ space", Matem. zametki, 1968; 3(2): pp. 157-164. (in Russian) doi:10.1007/BF01094328




DOI: https://doi.org/10.15421/240904

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2009 V.F. Babenko, R.O. Bilichenko

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


Registered in


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