复域中扰动Fejér点上Hermite——Fejér插值逼近的稳定性

该文在Jordan区域上研究扰动Fejér点上Hermite--Fejér插值对的逼近阶与收敛性, 完全解决了美国数学会 1991年Transactions of the AMS中Chui和Shen提出的问题,并将其边界条件J₂改进为.       

乘积的平方性

本文证明了乘积 (f(x)=ax²+bx+c∈Z[x]是二次不可约多项式)在n充分大时不是平方数.       

可变核Marcinkiewicz积分交换子在Herz型Hardy空间上的有界性

该文研究由可变核Marcinkiewicz 积分和Lip_β (Rⁿ)(0 <β≤ 1)函数生成的交换子μ_{Ω, b}. 证明了当可变核Ω∈L^∞(Rⁿ)×L^r(S^n-1)(r≥1)$时, 交换子μ_{Ω, b}从Herz型Hardy空间到Herz空间的有界性. 同时建立了参数型Marcinkiewicz 积分的交换子μ^ρ_{Ω, b}在Herz型Hardy空间上的有界性.     

Some Geometric Aspects of Operators Acting from L 1

We study some properties of the space (L₁,X) of all continuous linear operators acting from L₁ to a Banach space X. It is proved that every operator T ∈ (L₁, X) ``almost' attains its norm at the entire positive cone of functions supported at some suitable measurable subset , μ(A) > 0. Using this fact and a new elementary technique we prove that every operator T∈ (L₁) = (L₁, L₁) is uniquely represented in the form T= R+S, R, S∈ (L₁) , where R is representable and S possess a special property (*). Moreover, this representation generates a decomposition of the space (L₁) into complemented subspaces by means of contractive projections (the fact that the subspace of all representable operators is complemented in (L₁) was proved before by Z. Liu).     

ε-近似保正交映射的稳定性与扰动

对于Hilbert空间之间的ε-近似保正交线性映射T,给出了的一个估计,得到了ε-近似保正交线性映射的充分条件,研究了ε-近似保正交线性映射的稳定性,并获得了ε-近似保正交线性映射的扰动定理.       

内交换p-群的中心扩张(I)

设N,H为群. H被N的中心扩张是关于群的短正合序列:满足N≤Z(G).本文完全分类了当|N|=p,H为内交换p-群时, H被N的中心扩张所得的群.       

On A Hypergraph Turán Problem Of Frankl

Let be the 2k-uniform hypergraph obtained by letting P₁, . . .,P_r be pairwise disjoint sets of size k and taking as edges all sets P_i∪P_j with i ≠ j. This can be thought of as the ‘k-expansion’ of the complete graph K_r: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain can be obtained by partitioning V = V1 ∪V₂ and taking as edges all sets of size 2k that intersect each of V₁ and V₂ in an odd number of elements. Let denote a hypergraph on n vertices obtained by this construction that has as many edges as possible. For n sufficiently large we prove a conjecture of Frankl, which states that any hypergraph on n vertices that contains no has at most as many edges as . Sidorenko has given an upper bound of for the Tur′an density of for any r, and a construction establishing a matching lower bound when r is of the form 2^p+1. In this paper we also show that when r=2^p+1, any -free hypergraph of density looks approximately like Sidorenko’s construction. On the other hand, when r is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Turán density of to , where c(r) is a constant depending only on r. The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear algebra, the Kruskal–Katona theorem and properties of Krawtchouck polynomials. * Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship.     

中约化子空间上的仿射与伪仿射对偶小波标架

本文讨论中约化子空间上的仿射(伪仿射)对偶小波标架.我们建立了仿射系与伪仿射系之间的一个标架 和对偶标架保持定理,并且在没有任何衰减性假设的条件下获得了仿射(伪仿射)对偶小波标架在傅立叶域上的一个刻画.进一步, 我们也给出了仿射Parseval标架在傅立叶域上的刻画.       

The K?hler-Einstein metric for some Hartogs domains over symmetric domains

We study the complete K?hler-Einstein metric of a Hartogs domain built on an irreducible bounded symmetric domain sW, using a power N ^μ of the generic norm of Ω. The generating function of the K?hler-Einstein metric satisfies a complex Monge-Ampère equation with a boundary condition. The domain is in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X ε [0, 1[. This allows us to reduce the Monge-Ampère equation to an ordinary differential equation with a limit condition. This equation can be explicitly solved for a special value μ₀ of μ. We work out the details for the two exceptional symmetric domains. The special value μ₀ seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains.     

The argument shift method and the Gaudin model

We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U ( ) of a semisimple Lie algebra . This family is parameterized by finite sequences μ, z ₁, ..., z _n , where μ ∈ ^* and z _i ∈ ℂ. The construction presented here generalizes the famous construction of the higher Gaudin Hamiltonians due to Feigin, Frenkel, and Reshetikhin. For n = 1, the corresponding commutative subalgebras in the Poisson algebra S( ) were obtained by Mishchenko and Fomenko with the help of the argument shift method. For commutative algebras of our family, we establish a connection between their representations in the tensor products of finite-dimensional -modules and the Gaudin model. __________ Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 3, pp. 30–43, 2006 Original Russian Text Copyright ? by L. G. Rybnikov     

L_p-混合质心体和对偶L_p-混合质心体

本文引进了L_p-混合质心体Γ_(p,i)K、对偶L_p-混合质心体Γ_(-p,i)K和R~n中星体K和L的L_p-混合调和Blaschke加K+_pL的概念,成功地解决了L_p-混合质心体和对偶L_p-混合质心体的Shephard型问题.并且结合星体的L_p-混合调和Blaschke加的概念,分别建立了L_p-混合质心体的均质积分和对偶均质积分的Brunn-Minkowski型不等式.所获结论推广了已有文献的结果.     

(F_1,F_2)-攀援集的一些注记

研究(F_1,F_2)-攀援集的迭代不变性.定义了与正整数k相关的Furstenberg族的性质P(k)和Q(k).指出:对任意介于0,1之间的实数s而言,Furstenberg族M(s)具有性质P(k)和Q(k),其中■(s)表示非负整数集的所有上密度不小于s的无限子集构成的集族.据此证明了:对任意正整数k,S为系统(X,f)的(■(s),■(t))-攀援集当且仅当S为系统(X,f~k)的(■(s),■(t))-攀援集,其中s,t是介于0,1之间的任意给定的实数.     

套代数上的广义Jordan中心化子

设H是实数域或复数域F上的Hilbert空间,N为H上的非平凡套,τ(N)为相应的套代数,并且φ:τ(N)→τ(N)是一个可加映射.本文证明了如果存在正整数m,n,p,使得(m+n)φ(A~(p+1))=mφ(A)A~p+nA~pφ(A)或φ(A~(m+n+1))=A~mφ(A)A~n对所有的A∈τ(N)成立,则存在λ∈F,使得对所有的A∈τ(N),有φ(A)=λA.     

沿齐次曲线的强奇异积分算子在调幅空间上的有界性

设Γ_θ(t)为R~n(n≥2)中的齐次曲线,定义沿齐次曲线的强奇异积分算子T_(n,α,β)f(x)=p.v.∫_(-1)~1f(x-Γ_θ(t))(e~((-2πi|t|)~(-β))/(t|t|~α))dt,α,β>0.本文讨论了上述奇异积分算子在广义调幅空间上的有界性.     

Bernstein-Kantorovich算子逆中插式的强逆不等式

给出并证明了Bernstein—Kantorovich算子逆中插式的B型强逆不等式,即存在l,使得ω_φ~(2r)(f,1/n~(1/2))≤C(||k_n~((2r-1))f-f||_∞+||K_(ln)~((2r-1))f-f||_∞).     

海森堡群上薛定谔算子的黎斯位势的某些性质

设L=-△_(H~n)+V是Heisenberg群H~n上的Schr(o|¨)dinger算子,其中△_(H~n)为H~n上的次Laplacian,V≠0为满足逆H(o|¨)lder不等式的非负函数.本文研究H~n上Riesz位势I_α~L=L~(-α/2)在Campanato型空间A_L~β和Hardy型空间H_L~p上的某些性质.     

二次函数域理想类数问题的一个注记

应用F_q[t]上的Pell方程这一初等方法重新证明一个已知的结果:实二次函数域F_q(t)(D~(1/2))理想类数为1时,D只能为P或QR,其中P,Q,R是F_q[t]中的首一不可约多项式且Q,R次数为奇数.     

两类整环在w-算子下的刻画

通过对SM整环中准素w-理想与w-互素理想的讨论,证明了R是Krull整环当且仅当R是SM整环,w-dim(R)=1,且每个p-准素w-理想是素理想p的幂的w-包络.同时,运用w-算子,辅以t-,v-算子给出了π-整环的一些新的等价刻画.