This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset ...This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.展开更多
Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologi...Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologies on locally pseudocompact,locally precompact,or locally compact groups.We prove that each locally pseudocompact,connected topological group satisfies central subgroup paradigm,which gives an affirmative answer to a problem posed by Dikranjan,Tkachenko,and Yaschenko[Topology Appl.,2006,153:3338–3354].For a compact normal subgroup K of a locally compact totally disconnected group G,if G admits a transversal group topology,then G/K admits a transversal group topology,which gives a partial answer again to a problem posed by Dikranjan,Tkachenko,and Yaschenko in 2006.Moreover,we characterize some classes of locally compact groups that admit transversal group topologies.展开更多
For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amena...For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.展开更多
Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenabilit...Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.展开更多
In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases....In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.展开更多
This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolp...This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolpgical group with the axiom (A1).展开更多
In the compact group of galaxies the galaxies can merge into a few massive ones in a very short time, so they must be formed very recently. On the other hand, according to the theory of structure formation, the denser...In the compact group of galaxies the galaxies can merge into a few massive ones in a very short time, so they must be formed very recently. On the other hand, according to the theory of structure formation, the denser system should form earlier. By analyzing the apparent paradox, we suggest that the merging process of CDM halo plays an important role in the formation of the compact groups of galaxies: it delays the formation of compact groups of galaxies, and makes the pups of galaxies much denser.展开更多
In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we ob...In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.展开更多
In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Ha...In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.展开更多
In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dim...In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.展开更多
Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The gen...Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup>X of the space X which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every f in C(X,R) (the space of bounded continuous real valued functions on X) or Cc(X,R) (the space of continuous real valued functions on X with compact support) or the dual group <span style="white-space:nowrap;">Γ of the locally compact Abelian group G is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of f. Then X is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />.展开更多
In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the...In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.展开更多
In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a ...In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.展开更多
文摘This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.
基金This work was supported by the Key Program of the Natural Science Foundation of Fujian Province (No. 2020J02043)the National Natural Science Foundation of China (Grant No. 11571158)the Institute of Meteorological Big Data-Digital Fujian, and Fujian Key Laboratory of Data Science and Statistics.
文摘Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologies on locally pseudocompact,locally precompact,or locally compact groups.We prove that each locally pseudocompact,connected topological group satisfies central subgroup paradigm,which gives an affirmative answer to a problem posed by Dikranjan,Tkachenko,and Yaschenko[Topology Appl.,2006,153:3338–3354].For a compact normal subgroup K of a locally compact totally disconnected group G,if G admits a transversal group topology,then G/K admits a transversal group topology,which gives a partial answer again to a problem posed by Dikranjan,Tkachenko,and Yaschenko in 2006.Moreover,we characterize some classes of locally compact groups that admit transversal group topologies.
文摘For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.
文摘Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.
文摘In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.
文摘This paper is concerned with the relation between the compactness and sequential compactness in a topological space or a topological group, and show that the compactness and sequential compactness coincide in a topolpgical group with the axiom (A1).
基金Project partially supported by the Ministry of Science and Technology (of China).
文摘In the compact group of galaxies the galaxies can merge into a few massive ones in a very short time, so they must be formed very recently. On the other hand, according to the theory of structure formation, the denser system should form earlier. By analyzing the apparent paradox, we suggest that the merging process of CDM halo plays an important role in the formation of the compact groups of galaxies: it delays the formation of compact groups of galaxies, and makes the pups of galaxies much denser.
文摘In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.
文摘In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.
文摘In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.
文摘Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup>X of the space X which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every f in C(X,R) (the space of bounded continuous real valued functions on X) or Cc(X,R) (the space of continuous real valued functions on X with compact support) or the dual group <span style="white-space:nowrap;">Γ of the locally compact Abelian group G is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of f. Then X is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />.
基金NKBRSF CG 1990 3 2 80 5 National Natural Science F oundation of China !( No.5 98760 0 2 )
文摘In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.
基金Supported by the National Natural Science Foundation of China(11201414,11471153)
文摘In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X.
