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Main Authors: Aceska, Roza, Kim, Yeon Hyang, Narayan, Sivaram K.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.09013
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author Aceska, Roza
Kim, Yeon Hyang
Narayan, Sivaram K.
author_facet Aceska, Roza
Kim, Yeon Hyang
Narayan, Sivaram K.
contents 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 $F$.
format Preprint
id arxiv_https___arxiv_org_abs_2501_09013
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Dual Frame Completion Problem
Aceska, Roza
Kim, Yeon Hyang
Narayan, Sivaram K.
Functional Analysis
Representation Theory
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 $F$.
title Dual Frame Completion Problem
topic Functional Analysis
Representation Theory
url https://arxiv.org/abs/2501.09013