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Proceedings of the American Mathematical Society

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Harmonic analysis of harmonic functions in the plane

Author: L. A. Rubel
Journal: Proc. Amer. Math. Soc. 54 (1976), 146-148
MathSciNet review: 0390216
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Abstract | References | Additional Information

Abstract: A continuous function on the complex plane is harmonic if and only if the span of its compositions with entire functions is not dense in the space of continuous functions in the topology of uniform convergence on compact sets.

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

  • [1] L. A. Rubel and A. L. Shields, Hyperbolic mean automorphic functions, Invent. Math. 4 (1967), 294-298. MR 37 #1975. MR 0226385 (37:1975)
  • [2] L. Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math. (2) 48 (1947), 857-929. MR 9, 428. MR 0023948 (9:428c)

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Article copyright: © Copyright 1976 American Mathematical Society

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