Factorization for non-nevanlinna classes of analytic functions |
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Authors: | Eliyahu Beller |
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Institution: | (1) Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel |
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Abstract: | A generalization of the Blaschke product is constructed. This product enables one to factor out the zeros of the members of
certain non-Nevanlinna classes of functions analytic in the unit disc, so that the remaining (non-vanishing) functions still
belong to the same class. This is done for the classesA
−n (0<n<∞) andB
−n (0<n<2) defined as follows:f ∈A
−n iff |f(z)|≦C
f
(1−|z|)−n
,f ∈B
−n
iff |f(z)|≦exp {C
f
(1−|z|)−n
}, whereC
f
depends onf. |
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Keywords: | |
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