A. fryant, H. Shankar, "Fourier coefficients and growth of harmonic functions", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 614969, 10 pages, 1987. https://doi.org/10.1155/S0161171287000528
Fourier coefficients and growth of harmonic functions
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.
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.