Zeros of functions in weighted spaces with mixed norm

Sevast'yanov, E.; Dolgoborodov, A.
July 2013
Mathematical Notes;Jul2013, Vol. 94 Issue 1/2, p266
Academic Journal
In the spaces of analytic functions f in the unit disk with mixed norm and measure satisfying the Δ-condition, sharp necessary conditions on subsequences of zeros $\{ z_{n_k } (f)\} $ of the function f are obtained in terms of subsequences of numbers { n}. These conditions can be used to define, in the spaces with mixed norm, subsets of functions with certain extremal properties; these subsets provide answers to a number of questions about the zero sets of the spaces under consideration and, in particular, about weighted Bergman spaces.


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