Geodesic
Summability of trigonometric series and Calderon reproducing formulas
Publications de l'Institut Mathématique, _N_S_58 (1995) no. 72, p. 21 .

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We show how to associate a Calderon reproducing formula with a number of summability methods, including Abel-Poisson, Gaussian, Riesz typical and Bochner-Riesz means. Such formula contains local/global information concerning the trigonometric series being summed whether it be a Fourier series or not. Consequently a number of classical results of Littlewood--Paley type are unified as well as related results concerning the function class Fourier character of trigonometric series. The paper also provides classical insight and heuristics concerning much contemporary work falling under the name of wavelet analysis.
Classification : 42A24 42A16
Keywords: Calderon reproducing formulas, trigonometric series 
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     title = {Summability of trigonometric series and {Calderon} reproducing formulas},
     journal = {Publications de l'Institut Math\'ematique},
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     year = {1995},
     zbl = {0886.42002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1995_N_S_58_72_a3/}
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W.O. Bray. Summability of trigonometric series and Calderon reproducing formulas. Publications de l'Institut Mathématique, _N_S_58 (1995) no. 72, p. 21 . http://geodesic.mathdoc.fr/item/PIM_1995_N_S_58_72_a3/