Series Expansion and Reproducing Kernels for Hyperharmonic Functions

Abstract

First we show that any hyperbolically harmonic (hyperharmonic) function in the unit ball B in n has a series expansion in hyperharmonic functions, and then we construct the kernel that reproduces hyperharmonic functions in some L 1 B space. We show that the same kernel also reproduces harmonic functions inElsevier Science

A note on hyperharmonic and polyharmonic functions

“…In [7] it is shown that if f ∈ h(B N ) then there exists a unique sequence of harmonic homogeneous polynomials f k , of degree k, f k ∈ H k (R N ), such that…”