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

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American Mathematical Soc., 1986 - Mathematics - 78 pages
The book is based on lectures given by the author at a CBMS Regional Conference held in 1985. It presents the results about the construction of nonconstant inner functions in the unit ball in the $n$-dimensional complex space $C^n$. An appreciation of techniques not previously used in the context of several complex variables will reward the reader who is reasonably familiar with holomorphic functions of one complex variable and some functional analysis.

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1 The Pathology of Inner Functions
10 The Lsup1Modification Theorem
11 Approximation by Inner Functions
12 The LSC Property of Hsup
13 MaxSets and Nonapproximation Theorems
14 Inner Maps
15 A LusinType Theorem for AB
16 Continuity on Open Sets of Full Measure
17 Composition with Inner Functions

2 RWSequences
3 Approximation by EPolynomials
4 The Existence of Inner Functions
5 Radial Limits and Singular Measures
6 EFunctions in the Smirnov Class
7 Almost Semicontinuous Functions and ĂB
8 u + vf
9 Approximation in Lsup12
18 The Closure of AB in LHsuppB
19 Open Problems
Appendix I Bounded Bases in Hsup2B
Appendix II RWSequences Revisited
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