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On uniform interpolation sets

Published online by Cambridge University Press:  24 October 2008

J. P. Earl
J. P. Earl
Affiliation:
University of Kent
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Extract

A well-known result in the interpolation theory of integral functions (see Whittaker (16, 17), Pólya (14), Iyer (2), Pfluger (10)) states that an integral function of at most type K < ½π of order 2 bounded at the lattice points m + in (m, n = 0, ± 1, ± 2, … ) is necessarily constant. That the value ½π cannot be increased is shown by the Weierstrass σ-function. The result has, however, been generalized in several ways; the lattice points being replaced by more general sets and the bounded-ness condition by one of restricted rate of growth.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 721 - 742
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

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