New PDF release: Abstract Analytic Function Theory And Hardy Algebras

By K. Barbey, H. König

ISBN-10: 3540082522

ISBN-13: 9783540082521

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JENSEN Vo£M(~) INEQUALITY: w i t h 0<<8. log,Sd8 , ~ S u p { f l o g If S d @ # O t h e n t h e r e Thus In the case D P ( e ) > O BNM(~)%~ can be applied. as claimed. 7 we h a v e D P ( e ) = D P ( e m ) . such that o < < m for for all e 6 P o s ( X , Z ) . 3 in v i e w of D P ( m ) = I . upon w h i c h of DP(Fo) << some o 6 M ( ~ ) . as required. B : = { e } v = { o 6 c a ( X , Z ) :o<

Nals statement It r e q u i r e s lemma. complex O

5 ca(X,E) REMARK: Let c ca(X,Z) . Then be of is a band and = ii) E+F is a band and = iii) (EAF) ^ = iv) (E+F) ^ = E ^ n F ^. e 6 = bE I) It is e Ve6ca(X,Z). 7 {0} It = all I + For bands = = 0 Let s~t ]I811 is . Now implies + - E,F + observe that from 6 ca(X,Z) to prove i)~ii). and hence e = I. be Put < ~ I) a F ^. that e 6 F. For the obtain For e6E 6 F ^. bands Then = 8 will be written @BS=B trivial B^ = that ( U B s) ^ = s6I n Bs s6I • and and is = ii) and this (EQF) ^ = iii).

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Abstract Analytic Function Theory And Hardy Algebras by K. Barbey, H. König

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