摘要:We consider the space X of all analytic functions f(s1,s2)=∑∞m,n=1 amnexp(s1λm+s2μn) of two complex variables s1 and s2,equipping it with the natural locally convex topology and using the growth parameter,the order of f as defined recently by the authors.Under this topology X becomes a Frechet space.Apart from finding the characterization of continuous linear functionals,linear transformation on X,we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.
摘要:Let G be a locally compact Vilenkin group.In this paper we first establish the Hardy-Littlewood-Sobolev theorem on G.Then some boundedness theorems of fractional integral operators in Herz-type spaces on G are obtained.
摘要:We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets,thus obtaining explicit constants in a result of Levin.The estimates are then used to derive explicit lower bounds for exponential Riesz bases,as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem of Bogmer,Horvath,Joo and Seip.An application is discussed,where knowledge of explicit lower bounds of exponential Riesz bases in desirable.
摘要:Quasi-interpolation has been studied in many papers,e.g.,[5].Here we introduce nonseparable scaling function quasi-interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system.Several equivalent statements of accuracy of nonseparable scaling function are also given.In the numerical experiments,it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.
摘要:In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zeller operators for function of bounded variation.
摘要:In Sobolev space H2π-1 of periodic distributions,a multiresolution analysis is established,and then it is shown that a corresponding orthonormal basis generated by a single mother function except the first element.
摘要:In Sobolev space H2π^-1 of periodic distributions,a multiresolution analysis is established,and then it is shown that a corresponding orthonormal basis generated by a single mother function except the first element.
摘要:For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤l, or 0≤λ<1/2-1/2r(r≥2),0<a<r+10<a<(r+1)/1-λ, we obtain an equivalent theorem with ωuλρ(f ,t) instead of ωrλφ(f,t), where ωuφ(f,t) is theDitzian-Totik moduli of smoothness.
摘要:In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zeller operators for function of bounded variation.
摘要:Let function f (z) be analytic in |z|<1 and continuous on |z|≤1. The saturation class for the Jackson sums of the Bessel series of f(z) is discussed.
摘要:In this paper, we study the contraction linearity for metric projection in L p spaces. A geometrical property of a subspace Y of L p is given on which P Y is a contraction projection.
摘要:Lp(Rn) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the Lp(Rn) boundedness for the Marcinkiewicz integral are obtained.