Optimal recovery of convolution of n-functions from various classes by linear information

M.S. Gun'ko

doi:10.15421/241605

Optimal recovery of convolution of n-functions from various classes by linear information

M.S. Gun'ko (Oles Honchar Dnipropetrovsk National University)

Abstract

We found the optimal information and the optimal method of its use to recover the convolution of n-functions on some convex and centrally-symmetric classes of $$$2\pi$$$-periodic functions.

Keywords

recovery; convolution of n-functions; linear information

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References

Babenko V.F. "Optimal calculations of convolutions of functions from various classes", Proc. of International Conference on Constructive Function Theory (Varna, May 1989), Sofia, 1989; pp. 5-6. (in Russian)

Babenko V.F., Rudenko A.A. "On the optimal renewal of convolutions and scalar products of functions from various classes", Ukrainian Math. J., 1991; 43(10): pp. 1305-1310. (in Russian) doi:10.1007/BF01061804

Korneichuk N.P. Splines in approximation theory, Nauka, Moscow, 1984; 544 p. (in Russian)

Babenko V.F., Gun'ko M.S. "On the optimal recovery of convolution of n-functions by linear information", Ukrainian Math. J., 2016; 68(5): pp. 579-585. (in Russian) doi:10.1007/s11253-016-1248-8

Mairhuber J.C., Schoenberg I.J., Williamson R.E. "On variation diminishing transformations on the circle", Rend. Circ. mat. Polermo., 1959; 8(2): pp. 241-270. doi:10.1007/BF02843691

Karlin S. Total Positivity, Stanford Univ. Press, Stanford, California, 1968; Vol. 1: 540 p.

Babenko V.F. "Approximation of classes of convolutions", Siberian Math. J., 1987; 28(5): pp. 6-21. (in Russian) doi:10.1007/BF00969308

Pinkus A. "On n-width of periodic functions", J. Anal. Math, 1979; 35: pp. 209-235.