Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations - Bart, V. A.; Khavin, V. P. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
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.