H. Bohr's theorem for bounded symmetric domains
A theorem of Harald Bohr (1914) states that if f is a
holomorphic map from the unit disc into itself, then the sum of
absolute values of its Taylor expansion is less than 1 for
|z| < 1/3. The bound 1/3 is optimal. This result has been
extended in a suitable sense by Liu Taishun and Wang Jianfei
(2007) to the bounded complex symmetric domains of the four
classical series, and to polydiscs. The result of Liu and Wang
may be generalized to all bounded symmetric domains, with a
proof which does not depend on classification.
Version 2 (April 9, 2009):
References have been added, especially important references
[Ricci 1955] and [Bombieri 1962]. Section 1.2 has been
rewritten. Section 2.4 on open problems has been corrected.
Guy Roos < guy.roos@normalesup.org >