Abstract
The functions on Rd−1 × (0,∞) (d ≥ 3) that are annihilated by the Laplace–
Beltrami operator corresponding to the line-element dl2 = x2
d(dx21
+. . .+dx2
d) are
called modified harmonic. In this note, we prove a conjecture of Heinz Leutwiler
concerning the space of homogeneous modified harmonic polynomials of a fixed
degree.