Dans cette Note, nous donnons une preuve elementaire du lemme de Wiener pour les matrices infinies a decroissance polynomiale des termes non-digonaux.
In this Note, we give a simple elementary proof to Wiener's lemma for infinite matrices with polynomial off-diagonal decay.
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@article{CRMATH_2005__340_8_567_0, author = {Sun, Qiyu}, title = {Wiener's lemma for infinite matrices with polynomial off-diagonal decay}, journal = {Comptes Rendus. Math\'ematique}, pages = {567--570}, publisher = {Elsevier}, volume = {340}, number = {8}, year = {2005}, doi = {10.1016/j.crma.2005.03.002}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.03.002/} }
TY - JOUR AU - Sun, Qiyu TI - Wiener's lemma for infinite matrices with polynomial off-diagonal decay JO - Comptes Rendus. Mathématique PY - 2005 SP - 567 EP - 570 VL - 340 IS - 8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.03.002/ DO - 10.1016/j.crma.2005.03.002 LA - en ID - CRMATH_2005__340_8_567_0 ER -
%0 Journal Article %A Sun, Qiyu %T Wiener's lemma for infinite matrices with polynomial off-diagonal decay %J Comptes Rendus. Mathématique %D 2005 %P 567-570 %V 340 %N 8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.03.002/ %R 10.1016/j.crma.2005.03.002 %G en %F CRMATH_2005__340_8_567_0
Sun, Qiyu. Wiener's lemma for infinite matrices with polynomial off-diagonal decay. Comptes Rendus. Mathématique, Tome 340 (2005) no. 8, pp. 567-570. doi : 10.1016/j.crma.2005.03.002. http://archive.numdam.org/articles/10.1016/j.crma.2005.03.002/
[1] Nonuniform sampling and reconstruction in shift-invariant space, SIAM Rev., Volume 43 (2001), pp. 585-620
[2] R. Balan, P.G. Casazza, C. Heil, Z. Landau, Density, overcompleteness and localization of frames, Preprint, 2004
[3] The spectrum of integral operators on Lebesgue spaces, J. Operator Theory, Volume 18 (1987), pp. 115-132
[4] O. Christensen, T. Strohmer, The finite section method and problems in frame theory, J. Approx. Theory, in press
[5] Nonstationary tight wavelet frames II: unbounded intervals, Appl. Comput. Harmonic Anal., Volume 18 (2005), pp. 25-66
[6] Localization of frames II, Appl. Comput. Harmonic Anal., Volume 17 (2004), pp. 29-47
[7] A bound on the -norm of the -approximation by splines in terms of a global mesh ratio, Math. Comput., Volume 30 (1976), pp. 687-694
[8] Inverse of band matrices and local convergences of spline projections, SIAM J. Numer. Anal., Volume 14 (1977), pp. 616-619
[9] Commutative Normed Rings, Chelsea, New York, 1964
[10] Localized frames are finite unions of Riesz sequences, Adv. Comput. Math., Volume 18 (2003), pp. 149-157
[11] Localization of frames, Banach frames, and the invertibility of the frame operator, J. Fourier Anal. Appl., Volume 10 (2004), pp. 105-132
[12] Wiener's lemma for twisted convolution and Gabor frames, J. Amer. Math. Soc., Volume 17 (2003), pp. 1-18
[13] K. Gröchenig, M. Leinert, Symmetry of matrix algebras and symbolic calculus for infinite matrices, Trans. Amer. Math. Soc., in press
[14] Properiétés des matrices bien localisées prés de leur diagonale et quelques applications, Ann. Inst. H. Poincaré, Volume 7 (1990), pp. 461-476
[15] Using the refinement equations for the construction of pre-wavelets II: Powers of two, Curves and Surfaces (Chamonix-Mont-Blanc, 1990), Academic Press, Boston, MA, 1991, pp. 209-246
[16] A simple proof of Wiener's theorem, Proc. Amer. Math. Soc., Volume 48 (1975), pp. 264-265
[17] Rates of convergence for the approximation of shift-invariant systems in , J. Fourier Anal. Appl., Volume 5 (2000), pp. 519-616
[18] Four short stories about Toeplitz matrix calculations, Linear Algebra Appl., Volume 343/344 (2002), pp. 321-344
[19] Q. Sun, in preparation
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