TY - JOUR
AU - Brevig, Ole Fredrik
PY - 2016/11/01
Y2 - 2024/08/04
TI - Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 119
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-24745
UR - https://www.mscand.dk/article/view/24745
SP - 237-248
AB - 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 $1\leq p <2$.
ER -