Email this article The Range of the Berezin Transform
- Authors: Rao N.V.1
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Affiliations:
- University of Toledo
- Issue: Vol 228, No 6 (2018)
- Pages: 684-694
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240352
- DOI: https://doi.org/10.1007/s10958-017-3656-1
- ID: 240352
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Abstract
We give a description of all functions of the form \( \sum \limits_{i=1}^N{f}_i{\overline{g}}_i \) in the range of the Berezin transform, where fi and gi, 1 ≤ i ≤ N, are holomorphic functions on the unit disk ????, which generalizes the corresponding result of Ahern. We also give a very simple proof of the results of Ahern and the results due to Čučković and Li who deal with the special case N = 2 and g2 = zn.
About the authors
N. V. Rao
University of Toledo
Author for correspondence.
Email: rnagise@math.utoledo.edu
United States, 2801 W. Bancroft, Toledo, OH, 43606-3390
