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New Constructions of Functions Holomorphic in the Unit Ball of $C^{n}$

About this Title

Walter Rudin

Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 1986; Volume 63
ISBNs: 978-0-8218-0713-2 (print); 978-1-4704-2424-4 (online)
DOI: https://doi.org/10.1090/cbms/063
MathSciNet review: MR840468
MSC: Primary 32A35; Secondary 32A40

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Table of Contents

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Front/Back Matter

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Chapters

• 1. The Pathology of Inner Functions
• 2. RW-Sequences
• 3. Approximation by $E$-Polynomials
• 4. The Existence of Inner Functions
• 5. Radial Limits and Singular Measures
• 6. $E$-Functions in the Smirnov Class
• 7. Almost Semicontinuous Functions and $\widetilde {A}(B)$
• 8. $\vert u+vf \vert$
• 9. Approximation in $L^{1/2}$
• 10. The $L^1$-Modification Theorem
• 11. Approximation by Inner Functions
• 12. The LSC Property of $H^{\infty }$
• 13. Max-Sets and Nonapproximation Theorems
• 14. Inner Maps
• 15. A Lusin-Type Theorem for $A(B)$
• 16. Continuity on Open Sets of Full Measure
• 17. Composition with Inner Functions
• 18. The Closure of $A(B)$ in $(LH)^p(B)$
• 19. Open Problems
• Appendix I. Bounded Bases in $H^2(B)$
• Appendix II. RW-Sequences Revisited