Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series
Keyword(s):
For a real number $\alpha$ the Hilbert space $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of $n$. We extend a theorem of Seip on the bounded zero sequences of functions in $\mathscr{D}_\alpha$ to the case $\alpha>0$. Generalizations to other weighted spaces of Dirichlet series are also discussed, as are partial results on the zeros of functions in the Hardy spaces of Dirichlet series $\mathscr{H}^p$, for $1\leq p <2$.
2012 ◽
Vol 274
(3-4)
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pp. 1327-1339
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Keyword(s):
2005 ◽
Vol 71
(1)
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pp. 107-111
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2008 ◽
Vol 60
(5)
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pp. 1001-1009
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2012 ◽
Vol 09
(02)
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pp. 1260005
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