The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight by $$$A_{\alpha ,\beta }$$$-subspace

M.Ye. Tkachenko (Oles Honchar Dnipro National University),
V.O. Traktynskyi (Oles Honchar Dnipro National University)


The questions of the uniqueness of the best non-symmetric $$$L_1$$$-approximant with weight in the finite dimensional subspace  and the connection of such tasks with  $$$A_{\alpha ,\beta }$$$-subspaces were considered in this article. This result generalizes the known result of Kroo on the case of non-symmetric approximation.


$$$(\alpha ,\beta)$$$-approximation; KB-space; $$$L_1$$$-norm; weight; continuous functions

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Pinkus A. $$$L_1$$$-Approximation, Cambridge Univ. Press, 1989; 239 p.

Strauss H. "Unicity in $$$L_1$$$-approximation", Math. Zeitschr., 1981; 176: pp. 63-74. (in German) doi:10.1007/BF01258905

Tkachenko M.Ye., Traktynska V.M. "The uniqueness of the best non-symmetric $$$L_1$$$-approximant with a weight for continuous functions with values in KB-space", Res. Math., 2019; 27(1): pp. 67-74. doi:10.15421/241907

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ISSN (Online): 2664-5009
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