Geodesic
Cauchy Transforms of Arens Bounded Measures for a Vitushkin Amendment. I
Journal of convex analysis, Tome 16 (2009) no. 2, pp. 605-616.

Voir la notice de l'article provenant de la source Heldermann Verlag

We amend the theorem of A. G. Vitushkin [J. Functional Analysis 20 (1975) 149 - 157], who solves the problem of the rational approximation by constructive methods and a quasi-geometric notation -- the so called analytic continuous capacity -- , by a new sufficient condition. The proof is functional-analytic abstract and at the same time we can almost see the effects of the condition. We start with measures -- a structure bearing level beneath the AC-capacity -- and go by Cauchy transforms directly to the level of functions. Moreover we confirm a conjecture of J. Garnett [Duke Math. J. 37(1970) 689 - 699] for functions, which are continuous on the complex numbers C including infinity and analytic off a Cantor-set.
Classification : 46J10, 46J15
Mots-clés : Cauchy-Transform, new norm for measures, Vitushkin, rational approximation, Garnett's conjecture 
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     title = {Cauchy {Transforms} of {Arens} {Bounded} {Measures} for a {Vitushkin} {Amendment.} {I}},
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N. Trautmann. Cauchy Transforms of Arens Bounded Measures for a Vitushkin Amendment. I. Journal of convex analysis, Tome 16 (2009) no. 2, pp. 605-616. http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a16/