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A Central Limit Theorem for the L2 Error of Positive Wavelet by Ghora J.K.

By Ghora J.K.

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Séminaire Bourbaki, Vol. 43, 2000-2001, Exp. 880-893

Desk of Contents

Seminaire Bourbaki quantity forty three web page 1 2000-2001 [doi UNKNOWN] Laurent Bonavero -- Factorisation faible des functions birationnelles

Seminaire Bourbaki quantity forty three web page 39 2000-2001 [doi UNKNOWN] Marco Brunella -- Courbes entieres dans les surfaces algebriques complexes

Seminaire Bourbaki quantity forty three web page sixty three 2000-2001 [doi UNKNOWN] Michel Emery -- Espaces probabilises filtres : de los angeles theorie de Vershik au mouvement brownien, through des idees de Tsirelson

Seminaire Bourbaki quantity forty three web page eighty five 2000-2001 [doi UNKNOWN] Marc Herzlich -- Linegalite de Penrose

Seminaire Bourbaki quantity forty three web page 113 2000-2001 [doi UNKNOWN] Michele Audin -- Integrabilite et non-integrabilite de systemes hamiltoniens

Seminaire Bourbaki quantity forty three web page 137 2000-2001 [doi UNKNOWN] Pierre Cartier -- Fonctions polylogarithmes, nombres polyzetas et groupes pro-unipotents

Seminaire Bourbaki quantity forty three web page one hundred seventy five 2000-2001 [doi UNKNOWN] Antoine Chambert-Loir -- Theoremes d algebricite en geometrie diophantienne

Seminaire Bourbaki quantity forty three web page 211 2000-2001 [doi UNKNOWN] Philippe Michel -- Repartition des zeros des fonctions L et matrices aleatoires

Seminaire Bourbaki quantity forty three web page 249 2000-2001 [doi UNKNOWN] Michele Vergne -- Quantification geometrique et aid symplectique

Seminaire Bourbaki quantity forty three web page 279 2000-2001 [doi UNKNOWN] Philippe Biane -- Entropie libre et algebres d operateurs

Seminaire Bourbaki quantity forty three web page 301 2000-2001 [doi UNKNOWN] man Henniart -- Progres recents en fonctorialite de Langlands

Seminaire Bourbaki quantity forty three web page 323 2000-2001 [doi UNKNOWN] Emmanuel Peyre -- issues de hauteur bornee et geometrie des varietes

Seminaire Bourbaki quantity forty three web page 345 2000-2001 [doi UNKNOWN] Georges Skandalis -- Geometrie non commutative, operateur de signature transverse et algebres de Hopf

Seminaire Bourbaki quantity forty three web page 365 2000-2001 [doi UNKNOWN] Cedric Villani -- Limites hydrodynamiques de l equation de Boltzmann

Extra info for A Central Limit Theorem for the L2 Error of Positive Wavelet Density Estimator

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If G is a graph on Q then either G or its complement G complete graph whose vertex set is dense in an interval. Years later this was considerably extended by Galvin and Laver. After a good many somewhat ad hoc results, in 1956 Erd˝ os and Rado gave the first systematic treatment of “arrow relations” for cardinals; in their fundamental paper, “A partition calculus in set theory”, they set out to establish a ‘calculus’ of partitions. Among many other results, they proved that if λ ≥ 2 and ρ ≥ ℵ0 are cardinals then (λρ )+ → ((λρ )+ , (ρ+ )ρ )2 , but λρ ((λ · ρ)+ , ρ+ )2 .

It all started with his fascination with Sperner’s theorem on the maximal number of subsets of a finite set with no subset contained in another. Sperner proved in 1928 that if the ground set has n elements then the maximum is attained by the system of all n/2 subsets. Erd˝ os was quick to appreciate the beauty and importance of this result, and throughout his career frequently returned to problems in this vein. In 1939, Littlewood and Offord gave estimates of the number of real roots of a random polynomial of degree n for various probability spaces of polynomials.

Soon after the turn of the century, Landau, Hardy and Littlewood founded a flourishing branch of analysis by making extensive use of deep results resembling this theorem of Tauber. These Tauberian theorems claim that if a series is summable with a certain method of summation and satisfies certain additional conditions then it is also summable with a weaker method of summation. e. limx→∞ e−x sn xn /n! exists, where √ sn = a1 + . . + an ) and nan → 0 then an is convergent. The second part of the elementary proof of the PNT was, essentially, such a Tauberian theorem.

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