Wiener’s Lemma for Infinite Matrices Ii
نویسنده
چکیده
In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of B(`w), the algebra of all bounded linear operators on the weighted sequence space `w, for any 1 ≤ q <∞ and any discrete Muckenhoupt Aq-weight w. Constructive Approximation, To appear
منابع مشابه
Wiener’s lemma for infinite matrices with polynomial off-diagonal decay Le lemme de Wiener pour matrices infinies a decroissance polynomiale des termes non-diagonaux
In this note, we give a simple elementary proof to Wiener’s lemma for infinite matrices with polynomial off-diagonal decay.
متن کاملWiener’s Lemma for Infinite Matrices
The classical Wiener’s lemma and its various generalizations are important and have numerous applications in numerical analysis, wavelet theory, frame theory, and sampling theory. There are many different equivalent formulations for the classical Wiener’s lemma, with an equivalent formulation suitable for our generalization involving commutative algebra of infinite matrices W := {(a(j − j))j,j′...
متن کاملWiener’s Lemma: Localization and Various Approaches
Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play important roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved under inversion. In this introductory n...
متن کاملWiener’s Lemma: Pictures at an Exhibition
In this expository paper we present various general extensions of the celebrated Wiener’s Tauberian Lemma, outline several ingredients that are often used in proofs and discuss a few applications to localization of frames.
متن کاملar X iv : 0 70 5 . 43 04 v 1 [ m at h . FA ] 2 9 M ay 2 00 7 SLANTED MATRICES , BANACH FRAMES , AND SAMPLING
In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted matrices boundedness below of the corresponding operator in l for some p implies boundedness below in l for all p. We use the established result to enrich our u...
متن کامل