ON A THEOREM OF SZEGO

@inproceedings{Helson1955ONAT,
  title={ON A THEOREM OF SZEGO},
  author={Henry Helson},
  year={1955}
}
  • H. Helson
  • Published 1 February 1955
  • Mathematics
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… 

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The statement of the theorem is close to this result of Szegö : if a power series has coefficients assuming only finitely many distinct values, and if the analytic function so defined can be

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