Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

$\epsilon$-infinite frames for $k$-erasures

Document Type : Research Article

Authors
M. A. Hasankhani Fard 1
A. Nazari 2
1 Department of Mathematics, Vali-e-Asr University of Rafsanjan‎, ‎P.O. Box 546, Rafsanjan‎, ‎Iran.
2 Department of Pure Mathematics‎, ‎Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman‎, ‎P.O. Box 76169-14111, Kerman‎, ‎Iran.
10.30504/jims.2025.452123.1172
Abstract
Holmes and Paulsen studied finite frames from the viewpoint of coding theory‎. ‎In this paper, ‎for given $0<\epsilon\leq1$ and natural number $k$‎, ‎we introduce $\epsilon$-infinite frames for $k$-erasures in infinite-dimensional separable Hilbert space $\mathcal{H}$ from the of coding theory‎. ‎Additionally‎, ‎the perturbation and redundancy of $\epsilon$-infinite frames for $k$-erasures are studied‎.
Keywords
‎Frames‎
‎dual frames‎
‎erasures‎
‎redundancy‎
‎perturbation
Subjects
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Journal of the Iranian Mathematical Society
Volume 6, Issue 1
January 2025
Pages 91-105