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Additional resources for Analyse Complexe: Proceedings of the Journées Fermat - Journées SMF, held at Toulouse, May 24–27, 1983

Example text

Cr , la c o n d i t i o n (C1) ~ q u i v a u t GS\~c • Chaque ouvert % s u i t e il e x i s t e u n e f o n c t i o n p . s . h . 1 et de r a y o n e s t de R u n g e ,~ E C ~ ( ¢ n) (rn~Q 5 . ¢ N,~ >_ V sur Q5\~5, On d6finit a l o r s une f o n c t i o n U E P S H ( ¢ n) N C~°((r n - ~5) I U = V U = sup{V,N~) = N~ U et le e o u r a n t 2. TU CONSTRUCTION DE (q,q) , Soit sur Pc, sur Q5\~¢ sur (rn\~6, POTENTIELS GIX)BAUX 2 ~ q 2 .

Iz 1 [ = Iz 2i 5bD2(Z)=min{1-1zIt 2, 1-]z2 12}, z = (Zl,Z2) C D2 ~T2(z)=m~@_lz~[2 ~_lz212), z = (Zl,Z2) C D2 II. LES CLASSES Nct(D2) ET N(bD2). I~es e~sultats que nous donnons dans le paragvaphe sont identiques h ceux donn@s darts ~4]. Dans les 6nonc6s qui suivent, nous utiliserons la notation suivante : si un sous-ensemble analytique de pour tout p~el ~ ~- 0, D2, nous notons et si e X est est te courant d'int6gration sur X, 35 A(X,/~) = A(0 , U ) = ~ oh, d d s i g n e la m e s u r e d ' a i r e s u r dcrX THEOI~EME ].

W. on k. A~ors de fa~on admissible. La ddfinition d'une varidtd holomorphiquement tangente h l ' o r d r e dans [ 3 ] . mais sur la la quantit@ : PROPOSITION 2. soit ~ k-1. -k-c~ oz I OZ l (0) ~7 ~-~ @tant alors en particulier tangente h l'ordre +4( IzI Ik+', Tz,IIz21, Jz2i2), k-l. Dire que z converge 51 de faqon admissible vers O, que IImz21

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