Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp bo...Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp boundedness of such operators motivated by the open problem: Does σηfa,s→f for f ∈L1(O) (see M. H. Taible-son [6] and [5])?展开更多
In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpote...In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.展开更多
The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO syste...The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.展开更多
Let G be a connected unimodular Lie group, （?） be its Lie algebra which consists of all left invariant vector fields on G. Take a base {（?）<sub>j</sub>}<sub>1</sub><sup>n</sup>,...Let G be a connected unimodular Lie group, （?） be its Lie algebra which consists of all left invariant vector fields on G. Take a base {（?）<sub>j</sub>}<sub>1</sub><sup>n</sup>, of （?）, a Haar measure dy on G and a sub-Laplace operator （?）=sum from i,j to (a<sub>ij</sub>（?）<sub>i</sub>（?）<sub>j</sub>) on G, where展开更多
Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a t...Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？展开更多
Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation ...Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.展开更多
In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potent...In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.展开更多
文摘Based on a representation lemma. Riesz type kernels on the local field K and on the integer ring O in K are coitstructed. Furthermore, we discuss approximation theorems for the Lipschitz class Lip(L ;α) ana the Lp boundedness of such operators motivated by the open problem: Does σηfa,s→f for f ∈L1(O) (see M. H. Taible-son [6] and [5])?
基金the National Nature Science Foundation of China(10261002)
文摘In this article,the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups,and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups.
基金Supported partially by the NSF(61877039)the NSFC/RGC Joint Research Scheme of China(12061160462 and N_CityU102/20)the NSF of Zhejiang Province(LY19F020013)。
基金supported by the National Natural Science Foundation of China (Grant No.60873130)the Shanghai Leading Academic Discipline Project (Grant No.J50104)
文摘The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.
文摘Let G be a connected unimodular Lie group, （?） be its Lie algebra which consists of all left invariant vector fields on G. Take a base {（?）<sub>j</sub>}<sub>1</sub><sup>n</sup>, of （?）, a Haar measure dy on G and a sub-Laplace operator （?）=sum from i,j to (a<sub>ij</sub>（?）<sub>i</sub>（?）<sub>j</sub>) on G, where
文摘Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？
基金Supported by the Research Unit Matemática e Aplicac■s (UIMA) of University of Aveiro, Portugal
文摘Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical Hp spaces and the Hardy-Lorentz spaces H^p,q. Real interpolation results with function parameter are obtained, Based on them, the behavior of some classical operators is studied in this generalized setting.
文摘In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator.
