**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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