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Wednesday, 27. Nov. 2013 |
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15:15 – 16:15 |
Abstract
Rudin's
classic treatise "Function Theory in Polydiscs"
(1969) studies complex analysis on polydiscs starting
from the following question: How much of our extremely detailed knowledge about
holomorphic functions in the unit disc can be carried
over to an analogous situation in several variables, namely to polydiscs? A different perspective comes from the work of
H. Bohr and Bohnenblust--Hille
several decades earlier; here the main issue is function theory in the
infinite-dimensional polydisc or, more precisely,
estimates in finite-dimensional polydiscs that are
independent of the dimension. I will discuss some examples, old and new, of
what these different viewpoints have led to, as well as connections to other
areas.