Abstract:
We obtain sharp necessary conditions on the counting function of zeros of analytic functions from Bergman spaces with standard weight and from spaces which are their natural generalization.
Keywords:
analytic function, Bergman space of functions, counting function of zeros, Abel transformation, Jensen's inequality, Jensen's formula.
Citation:
A. A. Dolgoborodov, “On the Zeros of Functions from Bergman Spaces and Some Related Spaces”, Mat. Zametki, 88:2 (2010), 201–216; Math. Notes, 88:2 (2010), 183–197
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\by A.~A.~Dolgoborodov
\paper On the Zeros of Functions from Bergman Spaces and Some Related Spaces
\jour Mat. Zametki
\yr 2010
\vol 88
\issue 2
\pages 201--216
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\jour Math. Notes
\yr 2010
\vol 88
\issue 2
\pages 183--197
\crossref{https://doi.org/10.1134/S0001434610070187}
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Linking options:
https://www.mathnet.ru/eng/mzm8577
https://doi.org/10.4213/mzm8577
https://www.mathnet.ru/eng/mzm/v88/i2/p201
This publication is cited in the following 3 articles:
E. A. Sevast'yanov, A. A. Dolgoborodov, “Zeros of Functions in Weighted Spaces with Mixed Norm”, Math. Notes, 94:2 (2013), 266–280
A. A. Dolgoborodov, “Counting functions of zeros of analytic functions in spaces with mixed norm”, Russian Math. (Iz. VUZ), 56:10 (2012), 15–25
A. A. Dolgoborodov, E. A. Sevast'yanov, “Extremal properties of sequences of zeros of analytic functions in spaces with mixed norm”, Sb. Math., 202:8 (2011), 1085–1103