On zero sets in the Dirichlet space

Details On zero sets in the Dirichlet space On zero sets in the Dirichlet space

2011-02-28

arxiv.org/abs/1102.5596v1

Mathematics

Classical Analysis and ODEs

Journal of Geometric Analysis (2011)

Scientific paper

We study the zeros sets of functions in the Dirichlet space. Using Carleson
formula for Dirichlet integral, we obtain some new families of zero sets. We
also show that any closed subset of $E \subset \TT$ with logarithmic capacity
zero is the accumulation points of the zeros of a function in the Dirichlet
space. The zeros satisfy a growth restriction which depends on $E$.

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