Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
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J. Bonet, R. Braun, R. Meise, B. Taylor (1991)
Studia Mathematica
Józef Siciak (1997)
Annales Polonici Mathematici
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 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....
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