Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true...Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true.(2) It proved that the isomorphous relationship of the bottomgroups which guid to the hypergroup can still keep such relationship.(3) It proved that the basic isomorphous Theorem and the homogenous Theorem of the bottomgroup which raise to the hypergroup are still true.(4) It point out that when the isomorphous bottomgroups have been raised to the hypergroup,the conditions which form the isomorphism should be lessened.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
Jajcay's studies( 1993 ; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation ⊙ on the group Syme (G) , ...Jajcay's studies( 1993 ; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation ⊙ on the group Syme (G) , the stabilizer of the identity e ∈ G in the group Sym (G) . We prove that ( Syme (G) , ⊙) is a hypergroup and characterize the subhypergroups of this hypergroup.Finally, we show that the set of all subhypergroups of Syme ( G ) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut (G) .展开更多
Abstract. Let （R＋,＊,A） be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley g function and the Lusin area function for the Jacobi hypergroup and consider their （H^1, L^1 ） boundedness. Althou...Abstract. Let （R＋,＊,A） be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley g function and the Lusin area function for the Jacobi hypergroup and consider their （H^1, L^1 ） boundedness. Although the g operator for （R＋,＊,A） possesses better property than the classical g operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the （H^1,L^1） estimate for the Lusin area operator, a slight modification in its form is required.展开更多
In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R. Especia...In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R. Especially, we study the representation of the gener- alized translations of the product of two functions for these signed hypergroups.展开更多
文摘Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true.(2) It proved that the isomorphous relationship of the bottomgroups which guid to the hypergroup can still keep such relationship.(3) It proved that the basic isomorphous Theorem and the homogenous Theorem of the bottomgroup which raise to the hypergroup are still true.(4) It point out that when the isomorphous bottomgroups have been raised to the hypergroup,the conditions which form the isomorphism should be lessened.
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.
基金supported by National Natural Science Foundation of China (11001002, 10926061)the Beijing Foundation Program (201010009009, 2010D005002000002)+1 种基金supported by National Natural Science Foundation of China (10871003, 10990012)the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)
文摘In this article, we prove a heat kernel version of Hardy＇s theorem for the Laguerre hypergroup.
文摘Jajcay's studies( 1993 ; 1994) on the automorphism groups of Cayley maps yielded a new product of groups, which he called, rotary product. Using this product, we define a hyperoperation ⊙ on the group Syme (G) , the stabilizer of the identity e ∈ G in the group Sym (G) . We prove that ( Syme (G) , ⊙) is a hypergroup and characterize the subhypergroups of this hypergroup.Finally, we show that the set of all subhypergroups of Syme ( G ) constitute a lattice under ordinary join and meet and that the minimal elements of order two of this lattice is a subgroup of Aut (G) .
基金partly supported by Grant-in-Aid for Scientific Research (C) No.24540191, Japan Society for the Promotion of Science
文摘Abstract. Let （R＋,＊,A） be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley g function and the Lusin area function for the Jacobi hypergroup and consider their （H^1, L^1 ） boundedness. Although the g operator for （R＋,＊,A） possesses better property than the classical g operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the （H^1,L^1） estimate for the Lusin area operator, a slight modification in its form is required.
文摘In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R. Especially, we study the representation of the gener- alized translations of the product of two functions for these signed hypergroups.
