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Controlled Finite Frames
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Abstract
The finite frame theory is a very important part offrame theory due to its significant relevance in various branchesof mathematical applications. Studying controlled inite frames isthe goal of the work. To this end, we introduce controlled framesin a inite-dimensional Hilbert space and study some properties ofthem. The main class of inite frames in frame applied problemsis Parseval frames. By viewpoint to this, a brief discussion aboutParseval frames is presented and also Parseval controlled framesare investigated. Afterward, the paper characterizes all operatorsthat construct controlled inite frames. Furthermore, controlledinite frames are also considered as a proper subset of dual framesby the equivalency relation between frames.
Title: Controlled Finite Frames
Description:
Abstract
The finite frame theory is a very important part offrame theory due to its significant relevance in various branchesof mathematical applications.
Studying controlled inite frames isthe goal of the work.
To this end, we introduce controlled framesin a inite-dimensional Hilbert space and study some properties ofthem.
The main class of inite frames in frame applied problemsis Parseval frames.
By viewpoint to this, a brief discussion aboutParseval frames is presented and also Parseval controlled framesare investigated.
Afterward, the paper characterizes all operatorsthat construct controlled inite frames.
Furthermore, controlledinite frames are also considered as a proper subset of dual framesby the equivalency relation between frames.
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