On Various Moduli of Smoothness and K-Functionals
نویسندگان
چکیده
منابع مشابه
Equivalence of K-functionals and modulus of smoothness for fourier transform
In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.
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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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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 کاملequivalence of k-functionals and modulus of smoothness for fourier transform
in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.
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.
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2020
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-020-01848-0