On the integral representation of Herglotz and the trigonometric moment problem

Abstract

We may further suppose that ƒÏ(ƒÕ)-Rƒ3(0)ƒÕ/2ƒÎ is continued periodically beyond its original interval of definition with the period 2ƒÎ. In studying several problems on the class, it has been indicated that this re presentation formula often offers a powerful tool; cf., for instance, [8]. For the sake of later reference, we reproduce here the outline of its derivation. Applying first the Poisson integral representation to a function ƒ3(z)• ̧_??_ regular for |z|•...r<1, we get