International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 443-452
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 A. fryant and H. Shankar. 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.
We consider Harmonic Functions, of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity
in terms of its Fourier coefficients in case is not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in case is entire or non-entire.