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 
@article{JCA_2009_16_2_JCA_2009_16_2_a16,
     author = {N. Trautmann},
     title = {Cauchy {Transforms} of {Arens} {Bounded} {Measures} for a {Vitushkin} {Amendment.} {I}},
     journal = {Journal of convex analysis},
     pages = {605--616},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a16/}
}
TY  - JOUR
AU  - N. Trautmann
TI  - Cauchy Transforms of Arens Bounded Measures for a Vitushkin Amendment. I
JO  - Journal of convex analysis
PY  - 2009
SP  - 605
EP  - 616
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a16/
ID  - JCA_2009_16_2_JCA_2009_16_2_a16
ER  - 
%0 Journal Article
%A N. Trautmann
%T Cauchy Transforms of Arens Bounded Measures for a Vitushkin Amendment. I
%J Journal of convex analysis
%D 2009
%P 605-616
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a16/
%F JCA_2009_16_2_JCA_2009_16_2_a16
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/