On widths of some classes of functions with values in Hilbert space

S.V. Savela (Oles Honchar Dnipropetrovsk National University)

Abstract


We find the exact weak widths for one class of $$$2\pi$$$-periodic functions with values in Hilbert space, which is determined by moduli of continuity.

References


Babenko V.F. "Theorem on width of ball in spaces of mappings", Res. Math., 2009; 17: pp. 15-22. (in Russian)

Babenko V.F., Pichugov S.A. "Approximation of continuous vector functions", Ukrainian Math. J., 1994; 46(11): pp. 1435-1448. (in Russian) doi:10.1007/BF01058878

Dorogovtsev A.Ya. Periodic and stationary states of infinite-dimensional deterministic and stochastic dynamic systems, Kyiv, 1992. (in Russian)

Yosida K. Functional Analysis, 1967. (in Russian)

Kolmogorov A.N. "Uber die beste Annaherung von Funktionen einer gegebenen Funktionenklasse", Ann. of Math., 1936; 37(1): pp. 107-110. (in German) doi:10.2307/1968691

Lusternik L.A., Sobolev V.I. Short course on functional analysis, 1982. (in Russian)

Taikov L.V. "The best approximations of differentiable functions in the metric of $$$L_2$$$ space", Matem. zametki, 1977; 22(4): pp. 535-542. (in Russian) doi:10.1007/BF01146425

Tikhomirov V.M. "Set widths in functional spaces and theory of the best approximations", Uspekhi mat. nauk, 1960; 15(3): pp. 81-120. (in Russian) doi:10.1070/RM1960v015n03ABEH004093




DOI: https://doi.org/10.15421/240916

  

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