On Zero Sets in the Dirichlet Space |
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| Authors: | Karim Kellay Javad Mashreghi |
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| Affiliation: | 1. CMI, LATP, Universit?? de Provence, 39, Rue F. Joliot-Curie, 13453, Marseille Cedex 13, France
2. D??partement de math??matiques et de statistique, Universit?? Laval, Qu??bec, QC, Canada, G1K 7P4
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| Abstract: | We study the zero sets of functions in the Dirichlet space. Using Carleson??s formula for the Dirichlet integral, we obtain some new families of zero sets. We also show that any closed subset of $E subset mathbb {T}$ with logarithmic capacity zero is the set of 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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