Book Review: Moduli of smoothness
نویسندگان
چکیده
منابع مشابه
New Moduli of Smoothness
We discuss various properties of the new modulus of smoothness ω k,r (f, t)p := sup 0<h6t ‖W kh(·)∆khφ(·)(f , ·)‖Lp [−1,1], where φ(x) := √ 1− x2 and Wδ(x) = ( (1−x−δφ(x)/2)(1+x−δφ(x)/2) )1/2 . Related moduli with more general weights are also considered.
متن کاملOn Moduli of Smoothness of Fractional Order
In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.
متن کاملNew moduli of smoothness: weighted DT
We introduce new moduli of smoothness for functions f ∈ Lp[−1, 1]∩Cr−1(−1, 1), 1 ≤ p ≤ ∞, r ≥ 1, that have an (r − 1)st locally absolutely continuous derivative in (−1, 1), and such that φrf (r) is in Lp[−1, 1], where φ(x) = (1 − x2)1/2. These moduli are equivalent to certain weighted DT moduli, but our definition is more transparent and simpler. In addition, instead of applying these weighted ...
متن کاملWeighted moduli of smoothness of k-monotone functions and applications
Let ωk φ( f, δ)w,Lq be the Ditzian–Totik modulus with weight w, M k be the cone of k-monotone functions on (−1, 1), i.e., those functions whose kth divided differences are nonnegative for all selections of k + 1 distinct points in (−1, 1), and denote E(X, Pn)w,q := sup f ∈X infP∈Pn ∥w( f − P)∥Lq , where Pn is the set of algebraic polynomials of degree at most n. Additionally, let wα,β (x) := (1...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1988
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1988-15745-x