Extension and separation properties of positive definite functions on locally compact groups

Continuing earlier work, we investigate two related aspects of the set of continuous positive definite functions on a locally compact group . The first one is the problem of when, for a closed subgroup of , every function in extends to some function in . The second one is the question whether elements in can be separated from by functions in which are identically one on .

     

Embedding of a Cyclic Extension into a Cyclic Extension

A necessary and sufficient condition of the existence of a cyclic Galois extension of degree containing a given quadratic extension is found. Bibliography: 1 title.     

Extension of derivations

Any derivation of a properly infinite von Neumann algebra on a Hilbert space into the algebra of bounded operators on this space is implemented by a bounded operator.     

Extension Operators

We study the property of a domain of possesing extension operators bounded in the L²–norm of the gradients. We present known results as well as generalizations and refinements. We show how these results can be applied to the homogenization of perforated domains.     

域扩张时的李代数扩张

设E是特征零的代数封闭域,LE是E上L型有限维单李代效,F是E的包含素子域Q的子域,且|E:F]<∞.本文引入李代数的准子代数的概念,且F上同类型李代数LF就是LE的准子代数.本文定出了LE的包含LF的所有准子代数.     

解决矛盾问题的可拓模型与可拓知识的研究

可拓学是解决矛盾问题的学科,在可拓学的可拓模型原型的基础上,明确了计算机解决矛盾问题的可拓模型,它包括三部分:关联函数、可拓知识和推理算法,其中关联函数和可拓知识对不同的问题需要利用不同的原理,且它们是逐步变化的.在可拓知识中,关联函数的可拓变换需要通过计算证明其值是逐步增加的.这样,矛盾问题在计算机中才能得到解决.本文通过多个实例来说明解决矛盾问题的可拓模型及可拓知识的建立和实现.     

Extension of Hilbert's inequality

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.     

Extension of Transient Resolvents

For a submarkovian resolvent U=(U )_>0 with bounded initial kernel U ₀ on a Radon space X, we construct a minstable cone of potentials C on a compact metrizable space YX such that U extends to a subordonated (to C) resolvent on Y.     

Cauchy-Schwarz不等式的推广

在非负定矩阵的偏序意义下讨论了对Cauchy-Schwarz不等式的推广,将随机变量情形下的Cauchy-Schwarz不等式推广到随机向量情形,而且两个随机向量的维数不要求相等,一个是随机变量另一个是随机向量是其中的一个特殊情形,另外还研究了有限维空间中的向量情形的Cauchy-Schwarz不等式在矩阵情形下的推广,得到一个十分简明的结果,并将此结果用于讨论一类随机向量簇的协方差阵的下界,不仅得到下界的具体表达式,而且给出能达到该下界的充分必要条件.     

AT代数的拟对角扩张

Let A and B be C*-algebras. An extension of B by A is a short exact sequence 0 →A -→E→B→0. (*) Suppose that A is an AT-algebra with real rank zero and B is any .AT-algebra. We prove that E is an AT-algebra if and only if the extension (*) is quasidiagonal.     

Scalar Extension of Bicoalgebroids

After recalling the definition of a bicoalgebroid, we define comodules and modules over a bicoalgebroid. We construct the monoidal category of comodules, and define Yetter–Drinfel’d modules over a bicoalgebroid. It is proved that the Yetter–Drinfel’d category is monoidal and pre-braided just as in the case of bialgebroids, and is embedded into the one-sided center of the comodule category. We proceed to define braided cocommutative coalgebras (BCC) over a bicoalgebroid, and dualize the scalar extension construction of Brzeziński and Militaru (J Algebra 251:279–294, 2002) and Bálint and Szlachányi (J Algebra 296:520–560, 2006), originally applied to bialgebras and bialgebroids, to bicoalgebroids. A few classical examples of this construction are given. Identifying the comodule category over a bicoalgebroid with the category of coalgebras of the associated comonad, we obtain a comonadic (weakened) version of Schauenburg’s theorem. Finally, we take a look at the scalar extension and braided cocommutative coalgebras from a (co-)monadic point of view.      

Extension of Lai-Robbins-Wei's theorem

A theorem of Lai, Robbins and Wei^[7] is extended to a more general form to contain all the known results in the literature about the strong consistency of the least squares estimates of the progression coefficients in linear models with nonrandom regressors, and improvement is made on some of these results.