Dual Frame Completion Problem
Functional Analysis
2025-01-16 v1 Representation Theory
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 for a finite dimensional Hilbert space, and a set of vectors that is assumed to be a subset of a dual frame of , we answer the following question: Which dual frame for - if it exists - completes the given set ? Solutions are explored through a direct and an indirect approach, as well as via the singular value decomposition of the synthesis operator of .
Keywords
Cite
@article{arxiv.2501.09013,
title = {Dual Frame Completion Problem},
author = {Roza Aceska and Yeon Hyang Kim and Sivaram K. Narayan},
journal= {arXiv preprint arXiv:2501.09013},
year = {2025}
}