Softcover ISBN:  9780821807132 
Product Code:  CBMS/63 
List Price:  $36.00 
Individual Price:  $28.80 
eBook ISBN:  9781470424244 
Product Code:  CBMS/63.E 
List Price:  $34.00 
Individual Price:  $27.20 
Softcover ISBN:  9780821807132 
eBook: ISBN:  9781470424244 
Product Code:  CBMS/63.B 
List Price:  $70.00 $53.00 
Softcover ISBN:  9780821807132 
Product Code:  CBMS/63 
List Price:  $36.00 
Individual Price:  $28.80 
eBook ISBN:  9781470424244 
Product Code:  CBMS/63.E 
List Price:  $34.00 
Individual Price:  $27.20 
Softcover ISBN:  9780821807132 
eBook ISBN:  9781470424244 
Product Code:  CBMS/63.B 
List Price:  $70.00 $53.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 63; 1986; 78 ppMSC: Primary 32
The starting point for the research presented in this book is A. B. Aleksandrov's proof that nonconstant inner functions exist in the unit ball \(B\) of \(C^n\). The construction of such functions has been simplified by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of problems.
The lectures, presented at a CBMS Regional Conference held in 1985, are organized into a body of results discovered in the preceding four years in this field, simplifying some of the proofs and generalizing some results. The book also contains results that were obtained by Monique Hakina, Nessim Sibony, Erik Løw and Paula Russo. Some of these are new even in one variable.
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 with some functional analysis.
Readership 
Table of Contents

Chapters

1. The Pathology of Inner Functions

2. RWSequences

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. MaxSets and Nonapproximation Theorems

14. Inner Maps

15. A LusinType 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. RWSequences Revisited


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The starting point for the research presented in this book is A. B. Aleksandrov's proof that nonconstant inner functions exist in the unit ball \(B\) of \(C^n\). The construction of such functions has been simplified by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of problems.
The lectures, presented at a CBMS Regional Conference held in 1985, are organized into a body of results discovered in the preceding four years in this field, simplifying some of the proofs and generalizing some results. The book also contains results that were obtained by Monique Hakina, Nessim Sibony, Erik Løw and Paula Russo. Some of these are new even in one variable.
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 with some functional analysis.

Chapters

1. The Pathology of Inner Functions

2. RWSequences

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. MaxSets and Nonapproximation Theorems

14. Inner Maps

15. A LusinType 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. RWSequences Revisited