AVVISO
Il
ciclo di seminari di Analisi Armonica, proseguirà
Giovedì
18 maggio alle ore
sul
seguente argomento:
"Beurling
dimension and wave packets of
Wojtek Czaja
Università di
Vienna
Abstract
We
study wave packets $WP(\psi,M)$; that is, countable collections of
dilations, translations, and modulations of a single function $\psi $ in
$L^2(\R)$. The parameters of these unitary actions form a discrete subset
$M $ of $R^+ x R x R$. We introduce analogues of the notion of Beurling
density, adapted to the geometry of discrete subsets of $R^+ x R x R$, and
notions of lower and upper Beurling dimensions associated with these
densities. Our goal is to describe completeness properties of wave packets
via geometric properties of the sets of their parameters. In particular,
we show necessary conditions for $WP (\psi,M)$ to be a Bessel system, and we
construct multiple examples of non-standard wave packets with prescribed
dimensions.
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