Leírás
MEGHÍVÓ
az ELTE Analízis tanszék következő szemináriumi előadására
időpont: március 11. hétfő 12:15-13:15
helyszín: Déli tömb, 3-306
Előadó: Michal Rams (Varsó, IMPAN)
Title: Weighted Cesaro averages
Abstract: Given a sequence $(a_i)_i$, its Cesaro average
\[
a := \lim_{n\to\infty} \frac 1n \sum_{i=1}^n a_i
\]
is a useful concept (generalizing the idea of a limit of a sequence), defined in XIX century. Together with it, people were studying its weighted versions: for a nonsummable decreasing sequence of positive reals $(w_i)_i$ ({\it weights}) we define
\[
a_w := \lim_{n\to\infty} \frac 1 {\sum_{i=1}^n w_i} \sum_{i=1}^n w_i a_i.
\]
The most popular version of a weighted Cesaro average is the so-called {\it logarythmic average}, obtained for $w_i=1/i$.
It is well known that if the usual Cesaro average exists, so do the weighted versions, and they take the same value -- though there are sequences for which for example the logarythmic average exists but the Cesaro average does not. Surprisingly, it seems not to have been studied what is the relation between the choice of weights and the class of averageable sequences. We will investigate this, with a little multifractal corollary.
It is a joint work with Balazs Barany and Ruxi Shi.
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