منابع مشابه
Nonstandard Proofs of Herglotz, Bochner and Bochner-Minlos Theorems
We describe a unified approach to Herglotz, Bochner and BochnerMinlos theorems using a combination of Daniell integral and nonstandard analysis. The proofs suggest a natural extension of the last two theorems to the case when the characteristic function is not continuous. This extension is proven and is demonstrated to be the best one possible. The goal of this paper is to show how the classic ...
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If X is a topological space, and for m ≥ n the maps πm,n : X → X are defined by (πm,n(x))(j) = x(j), j ∈ {1, . . . , n}, then the spaces X and maps πm,n constitute a projective system, and its limit in the category of topological spaces is XN with the maps πn : X N → X, where XN has the initial topology for the family {πn : n ∈ N} (namely, the product topology). We say that a function f : XN → ...
متن کاملThe bilinear Bochner-Riesz problem
Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 − |ξ| − |η|)+ and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L × L into L with minimal smoothness, i.e., any δ > 0, and we obtain estimates for other pairs of spaces for...
متن کاملANALYSIS CLUB Bochner-Riesz Multipliers
We now consider the family of operators Tλ, λ ≥ 0, defined on Rn by T̂λ f (ξ) = mλ f̂ (ξ), where mλ(ξ) = (1− |ξ|)+. These are the Bochner-Riesz multipliers, which can be viewed as an attempt to smooth out the singularity of the disc multiplier to see if we can obtain boundedness on a wider range of Lp spaces. Note that when λ = 0 we obtain S1, and that as λ increases, the multiplier mλ becomes sm...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2012
ISSN: 1029-242X
DOI: 10.1186/1029-242x-2012-196