Zeros of functions in weighted Bergman spaces


Joel H. Shapiro


Michigan Math. J. 24 (1977), 243--265
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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