Dual Frame Completion Problem

Roza Aceska; Sivaram K. Narayan; Yeon Hyang Kim

Dual Frame Completion Problem

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arxiv 2501.09013 v1 pith:YMTBBCNL submitted 2025-01-14 math.FA math.RT

Dual Frame Completion Problem

Roza Aceska , Yeon Hyang Kim , Sivaram K. Narayan This is my paper

classification math.FA math.RT

keywords framedualgivenanswerapproachassumedassumptionscompletes

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In this paper we present the construction of an exact dual frame under specific structural assumptions posed on the dual frame. When given a frame $F$ for a finite dimensional Hilbert space, and a set of vectors $H$ that is assumed to be a subset of a dual frame of $F$, we answer the following question: Which dual frame $G$ for $F$ - if it exists - completes the given set $H$? Solutions are explored through a direct and an indirect approach, as well as via the singular value decomposition of the synthesis operator of $F$.

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