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Dual Frame Completion Problem

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

Roza Aceska , Yeon Hyang Kim , Sivaram K. Narayan This is my paper · ORCID
classification math.FAmath.RT
keywords framedualgivenanswerapproachassumedassumptionscompletes
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abstract

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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