A simple basis for $\mathcal{H}(n,k)$ is described in this question, however, not so symmetric as one may hope at a first glance, as it is shownin the answer. You may also want to check the beautiful (free online) textbook Harmonic Function Theory by Axley-Bourdon-Ramey.

A simple basis for $\mathcal{H}(n,k)$ is described in this question, however, not so symmetric as one may hope at a first glance, as it is shown in the answer. You may also want to check the beautiful (free online) textbook Harmonic Function Theory by Axley-Bourdon-Ramey.