关于Szeg?的一个不等式

设P_n(x)为[0,∞)上次数不超过n的代数多项式,则有‖p′_n(x)e^-x‖_[0,∞)≤(6.3n+1)‖p_n(x)e^-x‖_[0,∞).若p_n(x)同时又是奇函数或偶函数,则有‖p′_n(x)e^-x‖_[0,∞)≤(1.8+7n^1/2)‖p相似文献   

关于2n-算子组(LA,RB)的Taylor谱

设A=(A_1,……,A_n)与B=(B₁,……,B_n)为Hilbert空间H上的交换算子,L_A=(LA₁),……,LA_n))当R_B=(R(B₁,……,RB_n)分别为对应的B(H)中的左乘和右乘算子组。本文的主要结果是它们的Taylor谱有 Sp(L_A,R_B)=Sp(A)×Sp(B),
Sp_e(L_A,R_B)=Sp_e(A)×Sp(B)USp(A)×SP_e(B), 而且当A,B为Fredholm时,成立ind(L_A,R_B)=ind(A)·ind(B*)。我们用解算子方程的方法来证明上述命题,而且对Banach空间时,也作了一些讨论。     

概率密度的均匀核估计与近邻估计的均方误差

In this paper we consider the Mean Square Error (MSE) of two uaual estimates of density function f(x) at a point x: The uniform kernel estimate f_n(x) and the NN estimate fn(x). we- show that when f is differentiable for sufficiently high order at x. these MSE can be expanded in a form E(f_n(x)-f(x))²=A₁(x)n^-4/5 +A₂(x)n^-1+A₃(x)n^-6/5+…;E(f_n(x)-f(x))²=B₁(x)n^-4/5 +B₂(x)n^-1+B₃(x)n^-6/5+… And if we suitably choose the parameters in f_n and f_n to make A₁(x) and B₁(x)to assume its minimunm value, then we also, have A₂(x) =B₂(x) but A₃(X) differs form B₃(X). This result shows that while the two estimates are not identical with respect to MSE. each one can be superior to the other in various special cases.     

顶点算子超代数及相关的结合代数的表示

设 V 是一个顶点算子超代数. 该文得到了一系列的结合代数A_n(V)(对任何n∈ 1/2 + Z₊(i∈ {0,1})). 也给出了A_n(V) -模但非A_n-1/2(V) -模的不可约模范畴和单的可容许的V -模的范畴之间的一一对应关系. 对于给定的A_n(V) -模但非A_n-1/2(V) -模U, 还构造了一类广义Verma可容许的V -模M_n(U). 进而利用结合代数的表示进一步研究了顶点算子超代数的表示论.     

一类量子Koszul 代数的Hochschild 上同调

本文利用组合的方法, 详细地计算了一类量子Koszul 代数Λ_q (q ∈ k \{0}) 的各阶Hochschild 上同调空间的维数, 清晰地刻划了代数Λ_q 的Hochschild 上同调的cup 积, 确定了代数Λ_q 的Hochschild上同调环HH^*(Λ_q) 模去幂零元生成的理想N 的结构, 证明了当q 为单位根时, HH^*(Λ_q)/N 作为代数不是有限生成的, 从而为Snashall-Solberg 猜想(即HH^*(Λ)/N 作为代数是有限生成的) 提供了更多反例.     

关于控制算子的若干注记

Let B(H) be the set of all bounded linear operators on a Hilbert space H. An operator T∈B(H) is called dominant if (T-λ)(T-λ)^*≤M_λ²(T-λ)^*(T-λ),?λ∈C.The numerical range of T is difined by W (T) = {(Tx, x): ‖x‖ = 1, x∈H}. In Section 1 some new characteristic of dominant operators are given. If C = AB - BA, we prove that O∈W(C)^- then A is a dominart or φ-quasihy ponor-mal. In Section 2 we prove that O∈σ_e(△_A^σ) if A is a dominant, where(?), we also prove that if A∈B(H) is a norm attaining Ф-quasihyponormal, then A has a non-trivial invariant subspace. In Section 3 we discuss the closeness of the range of bounded linear operator F_AB:X→AX-XB, and prove that R(δ_A)∩{A}′∩{Aⁿ}′=0, where δ_A:X→AX-XA.     

右半平面内解析函数的准确零(R)级

Let f(s)=(?)a_ne^-λ_m3(s=σ+it),0<λ_n↑+∞), where (?)(n/logU(λ_n))=E<+∞,(?)(log|α_n|/λ_n)=0.     

关于多元函数最佳逼近精确阶的Timan问题

关于找一个充分必要条件使Ω^k(f,1/σ)L_p(Rⁿ)=O(A_σ(f)L_p(Rⁿ)),σ→∞,成立的Timan问题被解决.这个条件是Q^k(f,δ)L_p(Rⁿ)=O(Ω^k+1(f,δ)L_p(Rⁿ)),δ→0.     

算子方程的解及算子张量积

本文讨论Hilbert空间上一类三阶二元算子方程组A^*AC = αA^*A² + βAA^*A;AA^*C = λA^*A² + γAA^*A,给出所有重交换的解(A,C).作为应用,得到算子张量积A(?)B+C(?)D和A₁(?)A₂(?)…(?)A_n为拟正规算子的充分必要条件.     

偶错位图的张量幂的最大独立集和自同构群

若A_n 是X := {1, 2,..., n} 上的偶置换构成的交错群, E_n 是X 上的偶错位集, 则Cayley 图AΓ_n := Γ(A_n, E_n) 称为偶错位图. 令AΓ_n^q 为q 个AΓ_n 的张量幂. 在本文中, 我们研究了AΓ_n^q 的连通性、直径、独立数、团数、色数和最大独立集等性质. 利用AΓ_n^q 最大独立集的结果, 我们完全确定了AΓ_n^q 的自同构群的结构.     

REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES

Let k be a field and A_n(ω) be the Taft's n²-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(A_n(ω)) of A_n(ω) is a ribbon Hopf algebra. In the previous articles, we constructed an n₄-dimensional Hopf algebra H_n(p, q) which is isomorphic to D(A_n(ω)) if p ≠ 0 and q = ω^?1 , and studied the irreducible representations of H_n(1, q) and the finite dimensional representations of H₃(1, q). In this article, we examine the finite-dimensional representations of H_n(l q), equivalently, of D(A_n(ω)) for any n ≥ 2. We investigate the indecomposable left H_n(1, q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in mod H_n(1, q), and the Auslander-Reiten-quiver of H_n(1 q).     

A semilattice structure for Arens products

Let (A,?) be a Banach algebra. Then for n∈?, A ⁽²ⁿ⁾ has 2 ⁿ Arens products. In this paper we study the relations between the Arens products on A ⁽²ⁿ⁾. Moreover, if P _n (A) denotes the set of all Arens products on A ⁽²ⁿ⁾, for n∈?, we show that $P(A)=\bigcup_{n=1}^{\infty} P_{n}(A)$ is a ∧-semilattice. Also, we study P(A) as an infinite commutative semigroup and P(A)?{?} as a free semigroup generated by two elements. Then we investigate amenability and weak amenability for their semigroup Banach algebras.     

The real spectrum of an ideal and KO-theory exact sequences

A construction in abstract real algebra is used to define invariants S _n(A) of commutative rings, with or without identity. If A=C(X) is the ring of continuous real functions on a compact space, then S _n(A) = k0^–n(X), and, for any A, S _n(A) Z[1/2]-W _n(A) Z[1/2], where the W _n(A) are the Witt groups of A. In addition, a short exact sequence of rings yields a long exact sequence of the groups S _n. The functors S _n(A) thus provide a solution of a problem proposed by Karoubi. This paper primarily deals with the exact sequences involving a ring A and an ideal I A. Work supported in part by NSF Grant DMS85-06816.     

Generic Modules Over a Class of Drinfeld's Quantum Doubles

Let k be a field and A _n (ω) be the Taft's n ²-dimensional Hopf algebras. When n is odd, the Drinfeld quantum double D(A _n (ω)) of A _n (ω) is a Ribbon Hopf algebra. In the previous articles, we constructed an n ⁴-dimensional Hopf algebra H _n (p, q) which is isomorphic to D(A _n (ω)) if p ≠ 0 and q = ω^?1, and studied the finite dimensional representations of H _n (1, q). We showed that the basic algebra of any nonsimple block of H _n (1, q) is independent of n. In this article, we examine the infinite representations of H ₂(1, ? 1), or equivalently of H _n (1, q)?D(A _n (ω)) for any n ≥ 2. We investigate the indecomposable and algebraically compact modules over H ₂(1, ? 1), describe the structures of these modules and classify them under the elementary equivalence.     

The K-Theory of C *-Algebras with Finite Dimensional Irreducible Representations

We study the K-theory of unital C^*-algebras A satisfying the condition that all irreducible representations are finite and of some bounded dimension. We construct computational tools, but show that K-theory is far from being able to distinguish between various interesting examples. For example, when the algebra A is n-homogeneous, i.e., all irreducible representations are exactly of dimension n, then K_*(A) is the topological K-theory of a related compact Hausdorff space, this generalises the classical Gelfand-Naimark theorem, but there are many inequivalent homogeneous algebras with the same related topological space. For general A we give a spectral sequence computing K_*(A) from a sequence of topological K-theories of related spaces. For A generated by two idempotents, this becomes a 6-term long exact sequence.     

Über Deformationen von analytischen Abbildungskeimen

The notion of deformations of germs of k-analytic mappings generalizes the one of deformations of germs of k-analytic spaces. Using algebraic terms, we prove:

1. The morphism f: A→B of analytic algebras is rigid, iff it is infinitesimally rigid. Moreover, this is equivalent to Ex_A (B,B)=0. This theorem generalizes a result of SCHUSTER [11].
2. Let A be a regular analytic algebra. Then f is rigid iff there exists a rigid analytic algebra B_o such that f is equivalent to the canonic injection A→A?B_o.
3. If f is “almost everywhere” rigid or smooth, then the injection Ext _B ^l (Ω_B|A, Bⁿ)→Ex_A(B, Bⁿ) is an isomorphism.

     

A note on matrix subalgebras containing a full Jordan block

Let A be a subalgebra of the full matrix algebra M_n(F), and suppose J∈A, where J is the Jordan block corresponding to xⁿ. Let $\text{S}$ be a set of generators of A. It is shown that the graph of $\text{S}$ determines whether A is the full matrix algebra M_n(F).     

SK1 of Azumaya algebras over Hensel Pairs

Let A be an Azumaya algebra of constant rank n ² over a Hensel pair (R, I) where R is a semilocal ring with n invertible in R. Then the reduced Whitehead group SK₁(A) coincides with its reduction SK₁(A/I A). This generalizes a result of Hazrat (J Algebra 305:687–703, 2006) to non-local Henselian rings.     

Computations of coefficients in the polynomials of Pade´approximations by solving systems of linear equations

We explore reliability, stability and accuracy of determining the polynomials which define the Pade´approximation to a given function h(x) by solving a system of linear equations to get the coefficients in the denominator polynomial B_n(x). The coefficients in the numerator polynomial A_m(x) follow directly from those for B_n(x). Our approach is in the main heuristic. For the numerics we use the models e^?x1n(1 +x), (1 +x)^{± 1/2} and the exponential integral, each with m=n. The system of equations, with matrix of Toeplitz type, was solved by Gaussian elimination (Crout algorithm) with equilibration and partial pivoting. For each model, the maximum number of incorrect figures in the coefficients is of the order n at least, thus indicating that the matrix becomes ill conditioned as n increases. Let δ_n(x)andω_n(x) be the errors in A_n(x) and B_n(x) respectively, due to errors in the coefficients of B_n(x). For x fixed, δ_n(x) and ω_n(x) and the corresponding relative errors increase as n increases. However, for a considerable range on n, the relative errors in A_n(x)B_n(x) are virtually nil. This has the following theoretical explanation. Now B_n(x)h(x) ?A_m(m) = 0 (x^{m+n+ 1}). It can be shown that ω_n(x)h(x) ? δ_m(x) = 0(x^{m+ 1}). In this sense both A_m(x)B_n(x)andδ_m(x)ω_n(x) are approximations to h(x). Thus if the difference of these two approximations and ω_n(x)B_n(x), the relative error in B_n(x), are sufficiently small, then the relative error in A_m(x)/B_n(x) is of no consequence.