The Remez inequality for linear combinations of shifted Gaussians
نویسندگان
چکیده
منابع مشابه
The Remez Inequality for Linear Combinations of Shifted Gaussians
Let Gn := ( f : f(t) = n X j=1 aje −(t−λj) , aj , λj ∈ R ) . In this paper we prove the following result. Theorem (Remez-Type Inequality for Gn). Let s ∈ (0,∞). There is an absolute constant c1 > 0 such that exp(c1(min{ns, ns2} + s)) ≤ sup f ‖f‖R ≤ exp(240(min{n1/2s, ns2} + s)) , where the supremum is taken for all f ∈ Gn satisfying m ({t ∈ R : |f(t)| ≥ 1}) ≤ s . We also prove the right higher ...
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Let Pn be the collection of all polynomials of degree at most n with real coefficients. A subtle Bernstein-type extremal problem is solved by establishing the inequality ‖U (m) n ‖Lq(R) ≤ (cm)n‖Un‖Lq(R) for all Un ∈ e Gn, q ∈ (0,∞], and m = 1, 2, . . . , where c is an absolute constant and e Gn := ( f : f(t) = N X j=1 Pmj (t)e −(t−λj )2 , λj ∈ R , Pmj ∈ Pmj , N X j=1 (mj + 1) ≤ n ) . Some relat...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2008
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004108001849