Wiener's type regularity criteria on the complex plane
Józef Siciak
Annales Polonici Mathematici, Tome 66 (1997), p. 203-221 / Harvested from The Polish Digital Mathematics Library
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We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that d(t-1E∩|z-a|≤1)≥const>0 for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is Hölder continuous.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:269964 
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Józef Siciak. Wiener's type regularity criteria on the complex plane. Annales Polonici Mathematici, Tome 66 (1997) pp. 203-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p203bwm/

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