Fourier coefficients and growth of harmonic functions. (English) Zbl 0657.31005

Fryant, A.; Shankar, H.

Int. J. Math. Math. Sci. 10, 443-452 (1987).

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.

MSC:

31B05	Harmonic, subharmonic, superharmonic functions in higher dimensions
42A16	Fourier coefficients, Fourier series of functions with special properties, special Fourier series

Keywords:

harmonic functions; Fourier coefficients; entire; radius of harmonicity; growth measures