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On the derivatives at the origin of entire harmonic functions

Published online by Cambridge University Press:  18 May 2009

D. H. Armitage
D. H. Armitage
Affiliation:
The Queen's University, Belfast BT7 1NN.
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If f is an entire function in the complex plane such that

where 0 ≤ α < 1, and all the derivatives of f at 0 are integers, then it is easy to show that f is a polynomial (see e.g. Straus [10]). The best possible result of this type was proved by Pólya [9]. The main aim of this paper is to prove two analogous results for harmonic functions defined in the whole of the Euclidean space Rn, where n ≥ 2 (i.e. entire harmonic functions).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 2 , July 1979 , pp. 147 - 154
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

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