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\begin{center}
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{\Large Department of Mathematics, BGU}
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{\Huge Colloquium}\\[0.2\baselineskip]
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\textbf{On} \emph{Tuesday, March 28, 2017}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}
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{\large\scshape Vitali Milman
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(Tel Aviv University)
}
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will talk about
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{\Large\bfseries Some Fundamental Operator Relations in Convex Geometry and Classical Analysis\par}
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\textsc{Abstract:}
The main goal of the talk is to show how some classical
constructions in Geometry and Analysis appear (and in a unique way)
from elementary and very simple properties. For example, the polarity
relation and support functions are very important and well known
constructions in Convex Geometry, but some elementary properties
uniquely imply these constructions, and lead to their functional
versions, say, in the class of log-concave functions. It turns out
that they are uniquely defined also for this class, as well as for
many other classes of functions.
In this talk we will use these Geometric results as an introduction
to the main topic which involves the analogous results in Analysis. We
will start the Analysis part by characterizing the Fourier transform
(on the Schwartz class in R\^{}n) as, essentially, the only map which
transforms the product to the convolution, and discuss a very
surprising rigidity of the Chain Rule Operator equation (which
characterizes the derivation operation). There will be more examples
pointing to an exciting continuation of this direction in Analysis.
The results of the geometric part are mostly joint work with Shiri
Artstein-Avidan, and of the second, Analysis part, are mostly joint
work with Hermann Koenig.
The talk will be easily accessible for graduate students.
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