Fourier coefficients and growth of harmonic functions

Fourier coefficients and growth of harmonic functions

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We consider here 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 sukrensi.com 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.