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Title
Vector Valued Fourier Transforms and Fourier Type

Abstract
The central question of this talk is whether the methods of scalar-valued harmonic analysis can be transferred to the vector-valued setting. Fortunately, the answer of this question is negative. This opens the opportunity to classify Banach spaces (or operators) by measuring how well scalar-valued problems can be extended. More precisely, we ask if for a given Banach space $X$ and a locally compact Abelian group $G$, the $X$-valued Fourier transform on $G$ still satisfies a Hausdorff-Young inequality. Banach spaces having this property are said to be of Fourier type $p$ with respect to $G$. We will outline the theory around this property and describe new results in this direction.

Speaker(s)
Mariusz Piotrowski (CMUC/U. Coimbra)

Date
November 18, 2005

Time
14.30

Room
5.5

 
     
 

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