紧L-X半群上不同分布的组合乘积的极限性质

本文讨论一类紧拓扑半群上不同分布概率测度组合乘积的极限性质,利用“局部群化”的方法将紧群上,紧交换半群上的一些结果以相应的形式建立到紧L-X半群上.     

紧拓扑半群上概率测度卷积序列的极限性质

本文讨论紧拓扑半群上概率测度卷积序列的若干重要极限性质．在第１节中，我们讨论测度集的代数结构与其支撑集代数结构的关系．第２节的定理１，通过支撑集的代数结构给出组合收敛测度序列的一个极限定理．在定理２中我们讨论独立同分布时的情形，建立了一类紧半群上的Ｋａｗａｄａ－Ｉｔ型结果．这些定理推广了紧群、紧交换半群、紧Ｌ－Ｘ半群上一些相应的结论．     

以酉辛群为特征边界的双曲空间的调和分析

§1.前言 本文采用四元数体的观点,讨论了以酉辛群USP(2n)为特征边界的双曲空间 {I-Z>0,ZJ=J}(1.1) 的调和函数论,从另一角度建立酉辛群上的Abel收敛定理的出发点。 §2.四元数体上的第一类典型域 华罗庚教授、万哲元教授“典型群”中建立了一般非交换体上方阵行列式理论。 四元数体的工阶方阵表示     

局部紧H半群上概率测度序列的组合收敛性

首先讨论可数离散H半群上组合收敛的概率测度序列的一些极限性质,证明了相关文献中关于组合收敛必要条件的一个猜想.其次当半群具有交换性时,在同分布场合建立了强Kloss准则,证明经适当的shift变换可使概率测度卷积幂序列收敛到某个不变测度.最后讨论具有紧核的局部紧H半群上的概率测度卷积序列聚点集的构造.这些结果推广和改进了一些已有的结论.     

具有拟不变测度的交换拓扑群上的正定函数

<正> §1.引言如所周知,拓扑群上的正定函数是研究拓扑群的酉表示的重要工具.对于交换的、具有平移不变测度(即 Haar 测度)的拓扑群,例如局部紧的拓扑群,群上的连续正定函数可以用连续特征标关于对偶群上某个测度的积分表示.对于不具有平移不变测度的交换拓扑群,并不是每个连续正定函数都可以用上述积分表示.因而对于不具有平移不变的交换拓扑群,对群上的连续正定函数较难研究,关于抽象调和分析中其余的问题也有类似情     

p-级数域上的取样定理

实数群R上的取样定理已有许多数学家研究过,P.L.Butzer在[1]中阐述了该课题的历史及主要结果。程民德、沈燮昌、周民强在[4]中建立了Walsh变换的相应结果。李世雄在[5]中建立了一类局部紧Abel群上的取样定理,推广了上面提到的两种情形,但他要求所讨论的拓扑群的对偶群具有紧生成者,故局部域(见[2])便不在他讨论的范围内,本文建立了一类特殊的局部域(p-级数域)上的取样定理。     

一类紧半群上概率测度卷积的弱收敛性

本文讨论紧半群上概率测度卷积幂的弱收敛性，将紧群上的Ｋａｗａｄａ－Ｉｔｏ型结果以相应的形式建立到一类紧半群上。本文的结论蕴含了［１］中的定理２．１．４与［２］中的定理１。     

一类紧半群上概率测度卷积幂的弱收敛性

本文讨论紧半群上概率测度卷积幂的弱收敛性，将紧群上的Ｋａｗａｄａ－Ｉｔ６型结果以相应的形式建立到一类紧半群上．本文的结论蕴含了［１］中的定理２．１．４与［２］中的定理１．     

秩为2的紧单Lie群的谱理论

<正> 记△为紧 Riemann 对称空间 M 上的 Laplace-Beltraml 算子.△作用在光滑函数空间 C~∞(M)上的谱理论是熟知的,但作用在 P 阶 C~∞外微分形式空间 C~∞((?)~PM),P=1,2,…,dimM 上的谱理论,知道的较少.已有结果为:S.Gallot 与 D.Meyer 及A.Lévy-Bruhl-Laperrière 于1975年解决了 M=S~n 的情形,后者于1977年又解决了M=P~n(C)的情形;随后于1978年 A.Ikeda 与 Y.Taniguci 用不同的方法得到与[2],[3]相同的结果;1981年 C.Tsukamoto 解决了 M 为 SO(n+2)/SO(2)×SO(n)及 Sp(n+1)/Sp(1)×Sp(n)的情形.B.Beers 与 R.Millman 于1977年解决了 M 为SU(2),SU(3),SO(3),SO(4),SO(5)的情形,从而在秩≤2的紧单 Lie 群中,仅有G_2这个情形还没有解决.本文给出一种方法来计算紧半单 Lie 群的谱.应用这个方法我们具体算出了紧单 Lie 群 G_2的所有谱.首先,在§1中我们证明了对一切单连通、连通、紧半单 Lie 群 G 有下面     

关于连续映射半群拓扑熵的一点注记

本文研究了度量空间中连续映射构成半群的拓扑熵.利用Patr′ao~([8])的方法,给出了度量空间中两种有限个连续映射构成的半群的拓扑d-熵的定义,比较了两种拓扑d-熵的大小.证明了局部紧致可分度量空间上有限个真映射构成的半群的拓扑d-熵和它的一点紧化空间上对应的拓扑熵相等.上面结果推广了Patr′ao的相应结论.     

On the Determinability of Mixed Abelian Groups by Their Endomorphism Semigroups

Mixed Abelian groups with isomorphic endomorphism semigroups are studied. In particular, the question of when the isomorphism of endomorphism semigroups of Abelian groups implies the isomorphism of the groups themselves is investigated.     

On local integrability and transience of convolution semigroups of measures

The analytic proof due to M. Itô of the Kesten-Ornstein transience criterion for continuous convolution semigroups of nonnegative contraction measures on a compactly generated Abelian locally compact group has been reworked and given a self-contained form. The new proof still relies on the existence of the equilibrium measure but dispenses with the complete maximum principle.     

On the decision problem for theories of finite models

An infinite extension of the elementary theory of Abelian groups is constructed, which is proved to be decidable, while the elementary theory of its finite models is shown to be undecidable. Tarski’s proof of undecidability for the elementary theory of Abelian cancellation semigroups is presented in detail. Szmielew’s proof of the decidability of the elementary theory of Abelian groups is used to prove the decidability of the elementary theory of finite Abelian groups, and an axiom system for this theory is exhibited. It follows that the elementary theory of Abelian cancellation semigroups, while undecidable, has a decidable theory of finite models.     

Archimedeaness and additive utility on totally ordered semigroups

We study problems concerning the existence of additive utility funtions defined on totally ordered semigroups. The existence of an additive utility function on a semigroup is characterized by means of conditions that are similar, but not equivalent, to Archimedeaness. This fact is used to analyze the existence of utility representations (not necessarily additive) on totally ordered Abelian groups. In this direction, we show that the positive cone of a representable totally ordered Abelian group admits a countable partition into Archimedean semigroups. All the semigroups in that partition are representable by means of a utility function, but at most one is additively representable. Communicated by M. W. Mislove     

The Word Problem in the Variety of Inverse Semigroups with Abelian Covers

The variety of inverse semigroups which possess E-unitary coversover Abelian groups coincides with the Mal'cev product of thevariety of semilattices and the variety of Abelian groups,andalso with the variety generated by semidirect products of semilatticesand Abelian groups. We show that this variety (and any varietyof inverse semigroups that contains this variety) has undecidableword problem.     

Definability of separable torsion-free Abelian groups by endomorphism semigroups

In the class of separable torsion-free Abelian groups, we describe those which are defined by their endomorphism semigroups.Translated fromAlgebra i Logika, Vol. 34, No. 5, pp. 523–530, September-October, 1995.     

Definability of Abelian groups by homomorphism groups and endomorphism semigroups

In the paper, the isomorphism problem for completely decomposable Abelian torsion-free groups of finite rank is treated under the assumption that the groups of homomorphisms of these groups into some Abelian group are isomorphic and, moreover, the endomorphism semigroups of the groups are isomorphic.     

Definability of vector groups by endomorphism semigroups

Some conditions for torsion-free Abelian groups to be isomorphic are found; the groups in question are decomposable into a direct product of rank 1 groups with isomorphic endomorphism semigroups.Translated fromAlgebra i Logika, Vol. 33, No. 4, pp. 422–428, July-August, 1994.     

Abelian and Hamiltonian groupoids

In this work, we investigate some groupoids that are Abelian algebras and Hamiltonian algebras. An algebra is Abelian if for every polynomial operation and for all elements a, b, [`(c)] \bar{c} , [`(d)] \bar{d} the implication t( a,[`(c)] ) = t( a,[`(d)] ) T t( b,[`(c)] ) = t( b,[`(d)] ) t\left( {a,\bar{c}} \right) = t\left( {a,\bar{d}} \right) \Rightarrow t\left( {b,\bar{c}} \right) = t\left( {b,\bar{d}} \right) holds. An algebra is Hamiltonian if every subalgebra is a block of some congruence on the algebra. R. J. Warne in 1994 described the structure of the Abelian semigroups. In this work, we describe the Abelian groupoids with identity, the Abelian finite quasigroups, and the Abelian semigroups S such that abS = aS and Sba = Sa for all a, b ∈ S. We prove that a finite Abelian quasigroup is a Hamiltonian algebra. We characterize the Hamiltonian groupoids with identity and semigroups under the condition of Abelianity of these algebras.