# On the properties of generalized frames

Anastasia Zakharova
Grenoble INP
FRANCE

given at  strobl07 (17.06.07)
id:  599
length:  min
status:  accepted
type:  poster
ABSTRACT:
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\vspace{1em} \textit{A. A. Zakharova}\\
\textbf{On the properties of generalized frames}

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The author introduces the notion of the generalized frame and
considers its properties. Discrete and integral frames represent
particular cases of generalized frames. Necessary and sufficient
conditions for a generalized frame to be an integral (discrete)
one are obtained. It is also proved that for any bounded
invertible operator $A$ from Hilbert space $H$ (also from
non-separable one) to $L_{2}(\Omega)$ (where $\Omega$ is a space
with countably additive measure) with inverse bounded, there
exists such a generalized system that $A$ translates any element
$x\in H$ to its expansion coefficient.

Key words: frame, dual frame, generalized system.

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