Weaving Riesz Bases

2024/04/02 by Cabrelli, Carlos, Molter, Ursula, Negreira, Felipe · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2404.02229

Abstract

This paper explores woven frames in separable Hilbert spaces with an initial focus on the finite-dimensional case. We begin by simplifying the problem to bases, for which we obtain a unique characterization. We establish a condition that is both necessary and sufficient for vector reconstruction, which applies to Fourier matrices. Furthermore, we show that these characterizations are still valid in the infinite-dimensional case, for Riesz bases. Finally, we obtain several results for weaving Riesz bases of translations.

Cited by

• Weaving Information Packets
• Principal Non-singularity of Fourier Matrices on \mathbb Z_p × \mathbb Z_q and \mathbb Z₂^k × \mathbb Z_q

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