THE RANGE OF THE BEREZIN TRANSFORM

摘要

We give a description of all functions of the form ~N∑_(i=1) f_ig_i in the range of the Berezin transform, where f_i and g_i, 1 ≤ i ≤ N, are holomorphic functions on the unit disk D, which generalizes the corresponding result of Ahern. We also give a very simple proof of the results of Ahern and the results due to Cuckovic and Li who deal with the special case N = 2 and g_2 = z~n. Bibliography: 9 titles.