In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of...In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.展开更多
In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
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.
The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the r...The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.展开更多
Let 0<A≤1/3 ,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the line, where 1(x)= AT, ψ1(x) = 1-λ+λx, x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact H...Let 0<A≤1/3 ,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the line, where 1(x)= AT, ψ1(x) = 1-λ+λx, x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K(λ).展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
We consider the space X of all analytic functionsof 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 auth...We consider the space X of all analytic functionsof 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.展开更多
In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterization...This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.展开更多
The order of approximation for Newman-type rational interpolation to |x| is studied in this paper. For general set of nodes, the extremum of approximation error and the order of the best uniform approximation are esti...The order of approximation for Newman-type rational interpolation to |x| is studied in this paper. For general set of nodes, the extremum of approximation error and the order of the best uniform approximation are estimated. The result illustrates the general quality of approximation in a different way. For thespecial case where the interpolation nodes are Xi=(i/n)r(i = 1,2,'' ,n;r>0) . it is proved that the exact order of approximation is O(1/n),O(1/nlogn) and O(1/nr), respectively, corresponding to O<r<1, r=1and r>l.展开更多
In this paper we use wavelets to characterize weighted Triebel-Lizorkin spaces. Our weights belong to the Muckenhoupt class A q and our weighted Triebel-Lizorkin spaces are weighted atomic Triebel-Lizorkin spaces.
The authors introduce a new kind of fractional integral operators, namely, the so called (θ,N)-type fractional integral operators, and discuss their boundedness on the Hardy spaces, the weak Hardy spaces and the Herz...The authors introduce a new kind of fractional integral operators, namely, the so called (θ,N)-type fractional integral operators, and discuss their boundedness on the Hardy spaces, the weak Hardy spaces and the Herz-type Hardy spaces.展开更多
Let G be a locally compact Vilenkin group. In this paper toe first establish the Hardy-Littlewood-Sobolev theorem on G. Then some boundedness theorems of fractional integral operators in Herz-type spaces on G are obta...Let G be a locally compact Vilenkin group. In this paper toe 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.展开更多
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...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.展开更多
In this paper, we study the factorization of bi-orthogonal Laurent polynomial wavelet matrices with degree one into simple blocks. A conjecture about advanced factorization is given.
In this article we consider the generalized shift operator defined byon compact group G and by help of this operator we define 'Spherical' modulus of continuity. So we prove Stechkin and Jackson type theorems.
In this paper, we study the factorization of bi-orthogonal Laurent polynomial wavelet matrices with degree one into simple blocks. A conjecture about advanced factorization is given.
For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is th...For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is the Ditzian-Totik moduli of smoothness.展开更多
We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we ...We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.展开更多
基金Project Supported by the national Natural Science Foundation of China(No.19871010,No.69973010).
文摘In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.
文摘In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.
基金The research was supported by the NSF of Henan Province.
文摘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.
基金Project 19871071 supported by Natural Science Foundation of China
文摘The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.
基金This work is supported partially by the foundation of the National Education Ministry, National
文摘Let 0<A≤1/3 ,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the line, where 1(x)= AT, ψ1(x) = 1-λ+λx, x∈[0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K(λ).
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
文摘We consider the space X of all analytic functionsof 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.
基金This research is supported by Zhejiang Provincial Natural Science Foundation of China.
文摘In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
基金The work of the author has been supported by the Deutache Forschungsgemeinschaft(DFG) under Grant Ho 1846/1-1
文摘This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
文摘The order of approximation for Newman-type rational interpolation to |x| is studied in this paper. For general set of nodes, the extremum of approximation error and the order of the best uniform approximation are estimated. The result illustrates the general quality of approximation in a different way. For thespecial case where the interpolation nodes are Xi=(i/n)r(i = 1,2,'' ,n;r>0) . it is proved that the exact order of approximation is O(1/n),O(1/nlogn) and O(1/nr), respectively, corresponding to O<r<1, r=1and r>l.
基金The projectsupported by NSF of China and the Foundation of Advanced Research Center of Zhongshan Universi-ty
文摘In this paper we use wavelets to characterize weighted Triebel-Lizorkin spaces. Our weights belong to the Muckenhoupt class A q and our weighted Triebel-Lizorkin spaces are weighted atomic Triebel-Lizorkin spaces.
基金Project was partially supported by Changde Normal University( No.0 0 ( 2 84 ) ) and the SEDF of China
文摘The authors introduce a new kind of fractional integral operators, namely, the so called (θ,N)-type fractional integral operators, and discuss their boundedness on the Hardy spaces, the weak Hardy spaces and the Herz-type Hardy spaces.
文摘Let G be a locally compact Vilenkin group. In this paper toe 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.
文摘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.
基金The Work was Partially Supported by NSFC# 69735 0 2 0
文摘In this paper, we study the factorization of bi-orthogonal Laurent polynomial wavelet matrices with degree one into simple blocks. A conjecture about advanced factorization is given.
基金This research has been supported by the Research Institute for Fundamental Sciences, Tabriz, I-ran.
文摘In this article we consider the generalized shift operator defined byon compact group G and by help of this operator we define 'Spherical' modulus of continuity. So we prove Stechkin and Jackson type theorems.
基金The work was partially supported by NSFC # 69735052
文摘In this paper, we study the factorization of bi-orthogonal Laurent polynomial wavelet matrices with degree one into simple blocks. A conjecture about advanced factorization is given.
基金Supported by the Hebei Provincial Natural Science Foundation of China(101090). Supported by the Major Subject Foundation of Hebei Normal University.
文摘For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤1. or 0≤λ≤1/2-1/2r(r≥2),0 <a<r+1/1-λ, we obtain an equivalent theorem with ω(?)(f,t) instead of ω(?)(f,t), where ω(?)(f,t) is the Ditzian-Totik moduli of smoothness.
基金Research Partially Supported by a Grant from DGES (MEC), Spain.
文摘We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.
