Bart V. A.
Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations
Ukr. Mat. Zh. - 1994. - 46, № 1-2. - pp. 100–127
In view of the well-known Szego - Kolmogorov - Krein theorems on weighted approximation by the functions with semibounded spectrum (on a circle or a line), an efficient construction is suggested, which enables one to realize these approximations. It is based on relations similar to the Carleman tor-mula reconstructing an analytic function in terms its trace on the boundary of the domain of definition.