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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.09013 |
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| _version_ | 1866910786071298048 |
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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 |