On zero sets in the Dirichlet space

2011/02/28 by Karim Kellay, Javad Mashreghi, Kellay, Karim +1
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CA #math.CV

paper · pdf · doi:10.48550/arxiv.1102.5596

Journal of Geometric Analysis (2011)

arxiv created 2011/02/28 · arxiv updated 2011/03/01

Abstract

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 ⊂ \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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