Wiener's lemma for infinite matrices with polynomial off-diagonal decay

By Qiyu Sun. 2005

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Wiener’s Lemma for Infinite Matrices II (2007, methodology): “For 1 ≤ p ≤ ∞, the class Sp,u(Z,Z) was introduced by Sun for polynomial weights u := ((1 + |i− j|∞))i,j∈Zd with α > d(1− 1/p) in [41] and for any weighted matrix u in [43].”
SLANTED MATRICES, BANACH FRAMES, AND SAMPLING (2007, background): “This result has many extensions (see [7, 9, 10, 11, 30, 33, 34, 36, 37, 40, 41, 43] and references therein), some of which have been used recently in the study of localized frames [8, 32].”
Stability of Localized Operators (2008, background): “Therefore there are lots of papers devoted to the Wiener’s lemma for infinite matrices with various off-diagonal decay conditions (see [5,6,7,10,12,28,36,39,42,56,60,62] and also [37] for a short historical review).”