Zeros of functions in weighted
Bergman spaces
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Joel H. Shapiro
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Michigan Math.
J. 24 (1977), 243--265
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| Abstract: The main theorem is that for very general Bergman-type
spaces in the unit disc, if two of them corresponding to the
same weight are different, then their zero sets are different.
This generalizes previous work of Horowitz. The work here is
based on a construction with gap series that utilizes a method
of W. Rudin [Nederl. Akad. Wetensch. Proc. Ser. A 79 (1976)].
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