Naslov
Sequence dominance in shift-invariant spaces

Autori
Berić, Tomislav

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, kratko priopćenje, znanstveni

Skup
Zagreb Workshop on Operator Theory

Mjesto i datum
Zagreb, Hrvatska, 29.06.2020. - 30.06.2020

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Shift invariant systems, Bases, Frames, Riesz bases, Periodization function, Besselian property, Hilbertian property

Sažetak
For a given function $\psi \in L^2(\R)$ we study the system of integer translates $B_\psi = \left\{; ; T_k \psi : k \in \Z \right\}; ; $, where $T_k$ is the translation operator. Numerous properties of $B_\psi$ can be described via its periodization function $p_\psi(\xi) = \sum_{; ; k \in \Z}; ; \left| \widehat{; ; \psi}; ; (\xi + k) \right|^2$. For $\psi$ we define its associated coefficient space $\Cof_\psi$ as the set of all the sequences $\left( c_k \right)_{; ; k \in \Z}; ; $ for which $\sum c_k T_k \psi$ converges in the $L^2$ norm (with respect to the ordering $0, -1, 1, -2, 2, \ldots$ of $\Z$). There are two important special cases: when $\Cof_\psi$ contains $\ell^2(\Z)$, in which case we say that $B_\psi$ has the $(H)$--property, and when $\Cof_\psi$ is contained in $\ell^2(\Z)$, when we say that $B_\psi$ has the $(B)$--property. The $(B)$--property seems to be much more difficult to characterize and we will characterize it in two important special cases: when the periodization function has a certain degree of smoothness and when the system $B_\psi$ has the $(H)$--property alongside the $(B)$--property. This is joint work with Hrvoje Šikić.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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