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

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 | |

Back Cover | |

### Other editions - View all

New Constructions of Functions Holomorphic in the Unit Ball of CN, Volume 63 Walter Rudin Limited preview - 1986 |