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Description of Simple Exceptional Sets in the Unit Ball.
- Source :
- Czechoslovak Mathematical Journal; Mar2004, Vol. 54 Issue 1, p55-63, 9p
- Publication Year :
- 2004
-
Abstract
- For z ∈ ∂B<superscript>n</superscript>, the boundary of the unit ball in \Bbb {C}^n \ {\rm let} \ \Lambda(2)=\{ \lambda : \vert \lambda \vert \leqslan/math>. If f \in \Bbb{O}(B^n)</math> then we call E(f)=\{ z \in \partial B^n: \int_{\Lambda(z)} \vert f(z) \vert ^2 d\Lambda(z)=\infty \}</math> the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if E is a G<subscript>δ</subscript> and F<subscript>σ</subscript> subset of the projective (n − 1)-dimensional space \Bbb{P}^{n-1}=\Bbb{P}(\Bbb{C}^n)</math> then there exists a holomorphic function f in the unit ball B<superscript>n</superscript> so that E(f) = E. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00114642
- Volume :
- 54
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Czechoslovak Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 22101905