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Generalization of a classical theorem of Pólya and Szegő

Author: Ruben N. Mera
Journal: Proc. Amer. Math. Soc. 105 (1989), 666-669
MSC: Primary 30D15
MathSciNet review: 961414
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Abstract: An entire function of exponential type bounded on the real axis is bounded along every horizontal line. A generalization of this theorem to the class of entire functions of finite order is given.

References [Enhancements On Off] (What's this?)

  • [1] R. P. Boas, Jr., Entire functions, Academic Press, New York, 1954. MR 0068627 (16:914f)
  • [2] R. J. Duffin and A. C. Schaeffer, Some properties of functions of exponential type, Bull. Amer. Math. Soc. 44 (1938), 236-240. MR 1563717
  • [3] R. N. Mera, Entire functions of order larger than one, Auburn University dissertation, Auburn, AL, 1986.
  • [4] -, On the growth of analytic functions, J. Math. Anal. Appl. (to appear). MR 1087952 (92b:30032)
  • [5] E. Phragmén and E. Lindelöf, Sur une extension d'un principe classique de l'analyse et sur quelques proprietés des fonctions monogènes dans le voisinage d'un point singulier, Acta Math. 31 (1908), 381-406. MR 1555044
  • [6] M. Plancherel and G. Pólya, Fonctions entières et intégrales de Fourier multiples, Comment. Math. Helv. 9 (1937), 224-248, 10 (1938), 110-163. MR 1509570
  • [7] G. Pólya and G. Szegö, Problems and theorems in analysis, Springer-Verlag, Berlin, 1976.

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Keywords: Entire functions of exponential type, functions of order larger than one
Article copyright: © Copyright 1989 American Mathematical Society

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