Abstract
In this paper, the well-known results of Caratheodory, Toeplitz, F. Riesz, Herglotz, containing the characterization of the Caratheodory class with the aid of the Stieltjes integral and with the aid of nonnegative quadratic forms (conditions on the coefficients), are extended to certain other classes of functions, regular in a circle or in an annulus.
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