منابع مشابه
A Lower Bound Theorem
Motivated by Candes and Donoho′s work (Candés, E J, Donoho, D L, Recovering edges in ill-posed inverse problems: optimality of curvelet frames. Ann. Stat. 30, 784-842 (2002)), this paper is devoted to giving a lower bound of minimax mean square errors for Riesz fractional integration transforms and Bessel transforms.
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Let D(n) denote the cardinality of the largest subset of the set {1, 2, . . . , n} such that the difference of no pair of elements is a square. A well-known theorem of Furstenberg and Sárközy states that D(n) = o(n). In the other direction, Ruzsa has proven that D(n) & nγ for γ = 1 2 ( 1 + log 7 log 65 ) ≈ 0.733077. We improve this to γ = 1 2 ( 1 + log 12 log 205 ) ≈ 0.733412.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009435