ENGLISH

New constructions of functions holomorphic in the unit ball of Cn

By Walter Rudin

Book information

Publisher
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society
Year
1986
ISBN
0821807137, 9780821807132
ISSN
0160-7642
LCC
QA1 .R33 no. 63,QA331 .R33 no. 63
Open Library ID
OL2708630M
Language
english
Format
DJVU
Filesize
456 kB (466850 bytes)
Series
Regional conference series in mathematics 63
Pages
94\94
Library
Kolxo3
DPI
300
Time added
2009-12-04 00:34:26

Description

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 Low 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.

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