A
harmonic function
H on
is said to be
universal (in the sense of Birkhoff) if its set of translates
is dense in the space of all
harmonic functions on
with the topology of local uniform convergence. The main theorem includes the result that such
functions,
H, can have any prescribed order and type. The growth result is compared with a similar known theorem for G.D. Birkhoff's
universal holomorphic
functions and contrasted with known growth theorems for MacLane-type
universal harmonic and holomorphic
functions.