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Non-measurable interpolation sets

I. Integral functions

Published online by Cambridge University Press:  24 October 2008

M. E. Noble
M. E. Noble
Affiliation:
Queens' CollegeCambridge
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Extract

In two classical papers (1, 2) J. M. Whittaker introduced the study of integral functions bounded at the lattice points m + in(m, n = 0, ± 1, …,). He succeeded in showing (cf. also G. Polya(3)) that an integral function of at most the minimum type of order 2 uniformly bounded at the lattice points was necessarily constant. This result was improved almost simultaneously by A. Pflüger(5) and V. Ganapathy Iyer(11), who showed that the result was true also for functions of type K<½12π of order 2. The example of Weierstrass's σ(z) function shows that theirs is a best possible result in this direction.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 713 - 732
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

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