Hardy-Hilbert重级数定理的一个改进

利用Gram矩阵的正定性和Bernoulli不等式得到Holder不等式的一个加强的结果.由此建立了Hardy-Hilbert重级数定理的一个改进.特别,当p=2时,得到了经典的Hilbert重级数定理的一个很强的结果.     

A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra

As is well known, a Hopf algebra setting is an efficient tool to study some geometric structures such as the Maurer-Cartan invariant forms and the corresponding vector fields on a noncommutative space. In this study we introduce a two-parameter quantum (2+1)-superspace with a Hopf superalgebra structure.We also define some derivation operators acting on this quantum superspace, and we show that the algebra of these derivations is a Hopf superalgebra. Furthermore it will be shown how the derivation operators lead to a bicovariant differential calculus on the two- parameter quantum (2+1)-superspace. In conclusion, based on the bicovariant differential calculus, the Maurer-Cartan right invariant differential forms and the corresponding quantum Lie superalgebra are given.     

On the Behavior of a Power Series with Completely Multiplicative Coefficients near the Unit Circle

Power series whose coefficients are values of completely multiplicative functions from a general class determined by a small number of constraints are studied. The paper contains proofs of asymptotic estimates as such a power series tends to the roots of 1 along the radii of the unit circle, whence, in particular, it follows that these series cannot be extended beyond the unit disk.     

Classes of Graded Ideals with Given Data in the Exterior Algebra

Let ? be the family of graded ideals J in the exterior algebra E of a n-dimensional vector space over a field K such that e(E/J) = dim _K (E/J) = e, indeg(E/J) = i and H _E/J (i) = dim _K (E/J) _i are fixed integers. It is shown that there exists a unique lexsegment graded ideal J(n, e, i) ? ? whose Betti numbers give an upper bound for the Betti numbers of the ideals of ?. The authors continue the computation of upper bounds for the Betti numbers of graded ideals with given data started in Crupi and Utano (1999 Crupi , M. , Utano , R. ( 1999 ). Upper bounds for the Betti numbers of graded ideals of a given length in the exterior algebra . Comm. Alg. 27 : 4607 – 4631 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions

We introduce a non distributive algebra over the reals in 1 + 2 dimensions that contains the hyperbolic complex algebra ${\mathbb{H}_2}$ . The algebra has divisors of zero that can be avoided by introducing the necessary conditions. Under these conditions, the proposed addition and product operations satisfy group properties. More stringent restrictions sufficient to satisfy group properties separate the algebra in two subspaces. As an application, the composition of velocities in a deformed Lorentz metric is presented. In this approach, Minkowski light cones are deformed into light bipyramids.     

关于Hilbert空间单位球面上等距延拓的注记

本文指出,文[1]中有关在单位球面S1[H]上的1-Lipschitz假设条件减弱为“局部1-Lipschitz”条件时,那里的等距定理仍然成立.     

A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle

We prove a general Borg-type result for reflectionless unitaryCMV operators U associated with orthogonal polynomials on theunit circle. The spectrum of U is assumed to be a connectedarc on the unit circle. This extends a recent result of Simonin connection with a periodic CMV operator with spectrum thewhole unit circle. In the course of deriving the Borg-type result we also use exponentialHerglotz representations of Caratheodory functions to provean infinite sequence of trace formulas connected with the CMVoperator U.     

Banach Spaces of Universal Taylor Series in the Disc Algebra

We consider the problem of how to compute eigenvalues of a self-adjoint operator when a direct application of the Galerkin (finite-section) method is unreliable. The last two decades have seen the development of the so-called quadratic methods for addressing this problem. Recently a new perturbation approach has emerged, the idea being to perturb eigenvalues off the real line and, consequently, away from regions where the Galerkin method fails. We propose a simplified perturbation method which requires no á priori information and for which we provide a rigorous convergence analysis. The latter shows that, in general, our approach will significantly outperform the quadratic methods. We also present a new spectral enclosure for operators of the form A + iB where A is self-adjoint, B is self-adjoint and bounded. This enables us to control, very precisely, how eigenvalues are perturbed from the real line. The main results are demonstrated with examples including magnetohydrodynamics, Schrödinger and Dirac operators.     

单位圆周上（0，1，3）插值的一致收敛性

在本文中，我们考虑了将Ｌｅｇｅｎｄｒｅ多项式零点垂直映射到单位圆周时所得到的一组节点集上（０，１，３）插值的一致收敛性．     

A Theorem of Beurling-sLax Type for Hilbert Spaces of Functions Analytic in the Unit Ball

Schur multipliers on the unit ball are operator-valued functions for which the N-variable Schwarz-Pick kernel is nonnegative. In this paper, the coefficient spaces are assumed to be Pontryagin spaces having the same negative index. The associated reproducing kernel Hilbert spaces are characterized in terms of generalized difference-quotient transformations. The connection between invariant subspaces and factorization is established.     

单位圆内拟亚纯映射的Nevanlinna点

该文定义了单位圆内拟亚纯映射的Nevanlinna点与Borel点，并证明了单位圆内满足条件~lim_{r→1}{T(r)/{log1/(1-r)}}=∞的拟亚纯映射的Nevanlinna点与Borel点的存在性。     

几个关于二次域基本单位的结果

给出了当m是二个或三个素数之积时,二次域OK中有范数为-1单位的证明．还给出了m是其他值时的情况．     

Finite Dimensional Hopf Algebras Over the Dual Group Algebra of the Symmetric Group in Three Letters

We classify finite-dimensional Hopf algebras whose coradical is isomorphic to the algebra of functions on 𝕊₃. We describe a new infinite family of Hopf algebras of dimension 72.     

Hilbert $C^*$-模算子代数上Lie三重导子的刻画

假设$\mathcal A$是一个含单位元$e$的交换$C^*$-代数, $\mathcal M$是一个满的Hilbert $\mathcal A$-模. 令End_{$\mathcal A$}($\mathcal M$)表示$\mathcal M$上的全体有界$\mathcal A$线性算子构成的代数, $\mathcal M''$M表示$\mathcal M$到$\mathcal A$的全体有界$\mathcal A$线性映射构成的集合. 在本文中, 我们证明了如果存在$\mathcal M$中元素$x_0$和$\mathcal M''$中的元素$f_0$满足$f_0(x_0)=e$, 那么End_{$\mathcal A$}($\mathcal M$)上的$\mathcal A$-线性Lie三重导子都是标准的.     

A Basis for the Graded Identities of the Matrix Algebra of Order Two over a Finite Field of Characteristic p≠2

Let K be a finite field of characteristic p>2, and let M₂(K) be the matrix algebra of order two over K. We describe up to a graded isomorphism the 2-gradings of M₂(K). It turns out that there are only two nonisomorphic nontrivial such gradings. Furthermore, we exhibit finite bases of the graded polynomial identities for each one of these two gradings. One can distinguish these two gradings by means of the graded polynomial identities they satisfy.     

Nonuniqueness Sequences for Weighted Algebras of Holomorphic Functions in the Unit Circle

Suppose that is a system of continuous subharmonic functions in the unit disk and is the class of holomorphic functions f in such that log|f(z)| ≤ B _f p _f (z) + C _f , z ∈ , where B _f and C _f are constants and p _f ∈ . We obtain sufficient conditions for a given number sequence Λ = { λ_n} ⊂ to be a subsequence of zeros of some nonzero holomorphic function from , i.e., Λ is a nonuniqueness sequence for .__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova.