Dynamical sampling: mixed frame operators, representations and perturbations

2019/04/01 by Ehsan Rashidi, Rashidi, Ehsan, Abbas Najati +3
Computer Science · Mathematics · Medicine · #42C15 #47B40 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1904.00697

openalex publication_date 2019/04/01 · openalex created_date 2019/04/11 · openalex updated_date 2026/07/28

Abstract

Motivated by recent progress in operator representation of frames, we investigate the frames of the form \Tⁿ φ\_{n∈ I} for I=ℕ, ℤ , and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form \a_n Tⁿ φ\_n=0^∞ for some non-zero scalars \a_n\_n=0^∞ , and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form \Tⁿ φ\_n=0^∞.

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