On the range of the Berezin transform |
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Authors: | Patrick Ahern |
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Affiliation: | Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53705, USA |
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Abstract: | We study the range of the Berezin transform B. More precisely, we characterize all triples (f,g,u) where f and g are non-constant holomorphic functions on the unit disc D in the complex plane and u is integrable on D such that . It turns out that there are very ‘few’ such triples. This problem arose in the study of Bergman space Toeplitz operators and its solution has application to the theory of such operators. |
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