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Investigating the Bohr Problem Using Mathematica

Yakov Krasnov
Bar-Ilan University

Generalizing the classical Bohr result, we build, using Mathematica 3.0, the Bohr domains in multidimensional complex space--[Graphics:images/c_gr_1.gif] for the unit ball [Graphics:images/c_gr_2.gif], hypercone [Graphics:images/c_gr_3.gif], and polydisk [Graphics:images/c_gr_4.gif] correspondingly. This well-known problem in complex analysis is investigated to a new depth possible only with powerful Mathematica 3.0 computations.