On a Theorem of Szego
نویسنده
چکیده
is finite. Assume that the analytic function u(r, x) can be continued across some arc of the boundary of the unit circle. Then the ak are equal, beyond some point, to the terms of a periodic sequence. A number of generalizations and related results have been published [2; 3; 4; 5; 9], of which we mention in particular that of Duffin and Schaeffer [4]; these authors replace the hypothesis that u(r, x) is analytically continuable by the weaker assumption that the function is bounded in some sector of the circle. A theorem of the same type, but apparently not implied by the others, was proved in [5 ]: If the harmonic function
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