Abstract
We consider the well-known Szegö — Kolmogorov — Krein theorems on weighted approximations by functions with semibounded spectra defined on a circle or on a line and suggest an efficient construction that realizes these approximations. This construction is based on relations similar to the Cárleman formula for reconstructing analytic functions in terms of their traces on the boundary of their domains of definition.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 100–127, January–February. 1994.
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Khavin, V.P., Bart, V.A. Szegö-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Cárleman-type relations. Ukr Math J 46, 101–132 (1994). https://doi.org/10.1007/BF01057004
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DOI: https://doi.org/10.1007/BF01057004