Growth of Entire Harmonic Functions in R(superscript n), n≥2

10.6988/TOJMS.201011.0369

Devendra Kumar

Homogeneous harmonic polynomials ； Entire harmonic function ； Laplace's equation ； Lower order and lower type

Tamsui Oxford Journal of Mathematical Sciences

26卷4期（2010 / 11 / 01）

369 - 381

英文

Let h be a harmonic function on R(superscript n), n≥2. Then there exists on entire function f on C such that f(u)=h(u, 0, ...., 0) for all real u. This fact has been used to deduce theorems for harmonic function on R(superscript n) from classical results about entire functions. Moreover, we have considered the characterizations of lower order and lower type of h in terms of coefficients and ratio of these successive coefficients occurring in power series expansion of f.

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