Szegö-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Cárleman-type relations (Q1899477)

An explicit construction of approximants in the Szegö-Kolmogorov-Krein theorem (on the weighted approximation by functions with semibounded spectrum) is described. This construction is done with the help of new versions of the Carleman formula (the latter is an explicit expression allowing one to recover an analytic function by its boundary values on a set of positive length).