This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn...This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...展开更多
We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Rie...We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter's theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson's theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson's theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.展开更多
For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x±...For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used.展开更多
In this paper, we discuss the pointwise convergence of conjugate convolution op- erators with some applications to wavelets. Some criteria of convergence at (C, 1) continuous points, Lebesgue points and almost every...In this paper, we discuss the pointwise convergence of conjugate convolution op- erators with some applications to wavelets. Some criteria of convergence at (C, 1) continuous points, Lebesgue points and almost everywhere are established.展开更多
The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1<δ≤...The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1<δ≤ α+1/2 is obtained. With the aid of the generalized translation in terms of Jacobi polynomials, pointwise convergence theorems of the (C,δ) means for δ>α+1/2 and equiconvergence theorems for - 1<δ≤α+1/2 are proved. The analogues of the Lebesgue, Salem and Young theorems of the Cesaro means at the critical index δ = α+1/2 are established.展开更多
In this paper, strong summability of Cesaro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are anal-ogo...In this paper, strong summability of Cesaro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are anal-ogous to those of single and multiple Fourier series.展开更多
Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.
For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, ...For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property.展开更多
Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that poi...Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that pointwise convergence is maintained by all well-known impact bundles(such as the h-,g-,and R-bundle)and that theμ-bundle even maintains uniform convergence.Based on these results,a classification of impact bundles is given.Research limitations:As for all impact studies,it is just impossible to study all measures in depth.Practical implications:It is proposed to include convergence properties in the study of impact measures.Originality/value:This article is the first to present a bundle classification based on convergence properties of impact bundles.展开更多
In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form:Tλ(f;x)=B∫AKλ(t,x,f(t)...In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form:Tλ(f;x)=B∫AKλ(t,x,f(t))dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as (x,λ) → (x0, λ0) in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]展开更多
In this paper we study the convergence in norm and pointwise convergence of wavelet expansion in the Orlicz spaces,and prove that,under certain conditions on the wavelet,the wavelet expansion converges in the Orlicz-n...In this paper we study the convergence in norm and pointwise convergence of wavelet expansion in the Orlicz spaces,and prove that,under certain conditions on the wavelet,the wavelet expansion converges in the Orlicz-norm and also converges almost everywhere.展开更多
In this paper,we show that the Boussinesq operator B_(t)f converges pointwise to its initial data.f∈H^(s)(R)as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that th...In this paper,we show that the Boussinesq operator B_(t)f converges pointwise to its initial data.f∈H^(s)(R)as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that the optimal convergence index sc,1=1/4;on the other hand,we find that the Hausdorff dimension of the divergence set for B_(t)f isα1,b(s)={1-2s,as1/4≤s≤1/2;1,as 0<s<1/4.Moreover,a higher dimensional lift was also obtained for f being radial.展开更多
In this paper, we discuss tightness and fan tightness of multifunction spaces with pointwise convergence topology or compact-open topology, and generalize some results on con- tinuous single-valued function spaces to ...In this paper, we discuss tightness and fan tightness of multifunction spaces with pointwise convergence topology or compact-open topology, and generalize some results on con- tinuous single-valued function spaces to continuous multifunction spaces.展开更多
A series of convex functions on a Banach space is studied. The generalizations of the Moreau-Rockafellar theorem are given. As its application, the partial generalization of the Kuhn- Tucker theorem is obtained.
In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended be...In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m^p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.展开更多
基金supported by the NSF China#10571075NSF-Guangdong China#04010473+1 种基金The research of the second author was supported by Jinan University Foundation#51204033the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State education Ministry#2005-383
文摘This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...
基金Sponsored by Research Grant of the University of Macao No. RG024/03-04S/QT/FST
文摘We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter's theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson's theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson's theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.
文摘For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used.
文摘In this paper, we discuss the pointwise convergence of conjugate convolution op- erators with some applications to wavelets. Some criteria of convergence at (C, 1) continuous points, Lebesgue points and almost everywhere are established.
文摘The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1<δ≤ α+1/2 is obtained. With the aid of the generalized translation in terms of Jacobi polynomials, pointwise convergence theorems of the (C,δ) means for δ>α+1/2 and equiconvergence theorems for - 1<δ≤α+1/2 are proved. The analogues of the Lebesgue, Salem and Young theorems of the Cesaro means at the critical index δ = α+1/2 are established.
文摘In this paper, strong summability of Cesaro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are anal-ogous to those of single and multiple Fourier series.
文摘Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.
基金Supported by the Scientific Board of College of Nyiregyhaza
文摘For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property.
基金Supported by National Natural Science Foundation of China(Grant Nos.10671062,11071065 and 11171306)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20094306110004)Hu’nan Provincial Natural Science Foundation of China(Grant No.06JJ5012)
文摘In this paper, a new result on pointwise convergence of wavelets of generalized Shannon type is proved, which improves a theorem established by Zayed.
基金The author thanks Li Li(National Science Library,CAS)for drawing Figure 1.
文摘Purpose:A new point of view in the study of impact is introduced.Design/methodology/approach:Using fundamental theorems in real analysis we study the convergence of well-known impact measures.Findings:We show that pointwise convergence is maintained by all well-known impact bundles(such as the h-,g-,and R-bundle)and that theμ-bundle even maintains uniform convergence.Based on these results,a classification of impact bundles is given.Research limitations:As for all impact studies,it is just impossible to study all measures in depth.Practical implications:It is proposed to include convergence properties in the study of impact measures.Originality/value:This article is the first to present a bundle classification based on convergence properties of impact bundles.
文摘In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form:Tλ(f;x)=B∫AKλ(t,x,f(t))dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as (x,λ) → (x0, λ0) in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]
基金Supported by the Grant from Chongqing Education Commission (Grant No. KJ061201)
文摘In this paper we study the convergence in norm and pointwise convergence of wavelet expansion in the Orlicz spaces,and prove that,under certain conditions on the wavelet,the wavelet expansion converges in the Orlicz-norm and also converges almost everywhere.
基金supported by NSFC(Grant No.12071052)the Fundamental Research Funds for the Central Universitiessupported by the Research Initiation Fund for Young Teachers of Beijing Technology and Business University(Grant No.QNJJ2021-02)。
文摘In this paper,we show that the Boussinesq operator B_(t)f converges pointwise to its initial data.f∈H^(s)(R)as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that the optimal convergence index sc,1=1/4;on the other hand,we find that the Hausdorff dimension of the divergence set for B_(t)f isα1,b(s)={1-2s,as1/4≤s≤1/2;1,as 0<s<1/4.Moreover,a higher dimensional lift was also obtained for f being radial.
基金the Science and Research Foundation of Hangzhou Normal University (No.02010180)
文摘In this paper, we discuss tightness and fan tightness of multifunction spaces with pointwise convergence topology or compact-open topology, and generalize some results on con- tinuous single-valued function spaces to continuous multifunction spaces.
文摘A series of convex functions on a Banach space is studied. The generalizations of the Moreau-Rockafellar theorem are given. As its application, the partial generalization of the Kuhn- Tucker theorem is obtained.
基金supported by Consejo Nacional de Investigaciones Cientificas y Tecnicas(CONICET)and Universidad Nacional de San Luis(UNSL)with grants PIP(Grant No.11220110100033CO)PROICO(Grant No.30412)
文摘In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m^p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.