Download Analytic Functions and Manifolds in Infinite Dimensional by G. Coeuré (Eds.) PDF

By G. Coeuré (Eds.)

ISBN-10: 0444106219

ISBN-13: 9780444106216

Coeure G. Analytic features and manifolds in endless dimensional areas (NHMS, NH, 1974)(ISBN 0444106219)

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Extra resources for Analytic Functions and Manifolds in Infinite Dimensional Spaces

Example text

A Comment about (s3). Any h E S(A) has a restriction to which is weakly continuous for the pairing true ; any homomorphism from A which is weakly continuous in (El to o with p)Q A (sl) (El o p)A A , The converse is also - (a2) properties, has a continuation in S ( A ) by the Hahn-Banach theorem. - a) The series a Vh ha(f) , C hn(f) h:(g) is summable, for all n>,O,m>,~ a all f and g in A , Thus, we have : . ha(g) = C C n >,O ptq=n . g) So, ha t zb'e Vh . in E with the requirements of the proposi- b) Given a and b tion then za Vh is a homomorphism, all (a , all [zI < r , IzlI < , for a r suitable r > l .

V . s . E s p r e a d o v e r a n o t h e r complex c . v . s . - . OE(W for P r o o f . - Given f be g i v e n . - a s a n e x t e n s i o n of Suppose [17,48,80]. for . The mapping (6y(Y,F) . For i s contained i n v a n i s h e s and t h e r e f o r e t h e r a n g e o f thus, is an e x t e n s i o n Every OX(X,F)-extension Y f o r W E ( F ) 6 x ( ~ ,and ~ )h a s belongs t o 5 f and a m a n i f o l d (X,p) F 0 y(Y,6? a = . 5 E aoY aoo ; m e t r i z a b l e then t h e s e t o f exten- E 6 , ( @ ) and G E ( ~ ) a r e e q u a l .

1. I t is of degree i n the j t h variable. d. U be t h e monomial o f hence t h e r e e x i s t s (Elnad4 P 11 U* with z o e r / 2 U'* whose c o e f f i c i e n t i s 1. rU* at zo IP(zo)I >, . Iz 0 . Log. U4 u, and (dtl)" n Log(dt1) 6 . Log ( d t l ) ] 5 n . d . ( L 0 g . w)w-' Now, w e use t h e mean v a l u e i n t e g r a l i n P o i s s o n k e r n e l of a l l normalized . ,.. Log(dt1) . is u n i f o r m l y pz 0 HOLOMORPHIC CONVEXITY 38 Finally, for a suitable M Ad C mes. - Cover and Q be a compact subset o f a manifold Let and l e t f E bx(X,O;I.

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