On optimal estimate of the block orthogonal greedy algorithm for g-frames. (English) Zbl 1481.42040
In this paper, the authors study Lebesgue-type inequalities to obtain an optimal approximation (upper estimates for the errors and convergence) of the block orthogonal greedy algorithm with regard to g-frames in Hilbert spaces. Also, they obtain an accurate estimate involved in the errors of the block orthogonal greedy algorithm for g-frames analogous to the result obtained using dictionaries by E. D. Livshitz [J. Approx. Theory 164, No. 5, 668–681 (2012; Zbl 1248.41048)].
Reviewer: Anirudha Poria (Bengaluru)
MSC:
| 42C15 | General harmonic expansions, frames |
| 42C30 | Completeness of sets of functions in nontrigonometric harmonic analysis |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 46B15 | Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces |
Citations:
Zbl 1248.41048References:
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