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International Journal of Mathematics and Mathematical Sciences
Volume 10, Issue 3, Pages 443-452
http://dx.doi.org/10.1155/S0161171287000528

Fourier coefficients and growth of harmonic functions

1Department of Mathematics, Utica College of Syracuse University, Utica 13502, New York, USA
2Department of Mathematics, Ohio University, Athens 45701, Ohio, USA

Received 7 October 1986

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in case H is not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in case H is entire or non-entire.