共查询到20条相似文献,搜索用时 31 毫秒
1.
Sarah H. Ferguson 《Journal of Functional Analysis》1997,150(2):526-543
Results on first order Ext groups for Hilbert modules over the disk algebra are used to study certain backward shift invariant operator ranges, namely de Branges–Rovnyak spaces and a more general class called (W; B) spaces. Necessary and sufficient conditions are given for the groups Ext1A()(, (W; B)) to vanish whereis thedualof the vector-valued Hardy module, H2. One condition involves an extension problem for the Hankel operator with symbolB,ΓB, but viewed as a module map from H2into (W; B). The group Ext1A()(, (W; B))=(0) precisely whenΓBextends to a module map from L2into (W; B) and this in turn is equivalent to the injectivity of (W; B) in the category of contractive HilbertA()-modules. This result applied to the de Branges–Rovnyak spaces yields a connection between the extension problem for the HankelΓB and the operator corona problem. 相似文献
2.
Franois Nicoleau 《Journal de Mathématiques Pures et Appliquées》2006,86(6):463-470
We study a direct and an inverse scattering problem for a pair of Hamiltonians (H(h),H0(h)) on , where H0(h)=−h2Δ and H(h)=H0(h)+V, V is a short-range potential and h is the semiclassical parameter. First, we show that if two potentials are equal in the classical allowed region for a fixed non-trapping energy, the associated scattering matrices coincide up to O(h∞) in . Then, for potentials with a regular behaviour at infinity, we study the inverse scattering problem. We show that in dimension n3, the knowledge of the scattering operators S(h), , up to O(h∞) in , and which are localized near a fixed energy λ>0, determine the potential V at infinity. 相似文献
3.
Weight distribution of some reducible cyclic codes 总被引:1,自引:1,他引:0
Let q=pm where p is an odd prime, m3, k1 and gcd(k,m)=1. Let Tr be the trace mapping from to and . In this paper we determine the value distribution of following two kinds of exponential sums and where is the canonical additive character of . As an application, we determine the weight distribution of the cyclic codes and over with parity-check polynomial h2(x)h3(x) and h1(x)h2(x)h3(x), respectively, where h1(x), h2(x) and h3(x) are the minimal polynomials of π−1, π−2 and π−(pk+1) over , respectively, for a primitive element π of . 相似文献
4.
Kyo Nishiyama 《Advances in Mathematics》2011,(5):4338
Let G be a reductive algebraic group over C and denote its Lie algebra by g. Let Oh be a closed G-orbit through a semisimple element h∈g. By a result of Borho and Kraft (1979) [4], it is known that the asymptotic cone of the orbit Oh is the closure of a Richardson nilpotent orbit corresponding to a parabolic subgroup whose Levi component is the centralizer ZG(h) in G. In this paper, we prove an analogue on a semisimple orbit for a symmetric pair.More precisely, let θ be an involution of G, and K=Gθ a fixed point subgroup of θ. Then we have a Cartan decomposition g=k+s of the Lie algebra g=Lie(G) which is the eigenspace decomposition of θ on g. Let {x,h,y} be a normal sl2 triple, where x,y∈s are nilpotent, and h∈k semisimple. In addition, we assume , where denotes the complex conjugation which commutes with θ. Then is a semisimple element in s, and we can consider a semisimple orbit Ad(K)a in s, which is closed. Our main result asserts that the asymptotic cone of Ad(K)a in s coincides with , if x is even nilpotent. 相似文献
5.
Pao-Sheng Shen 《Statistics & probability letters》1998,40(4):87-361
Stute and Wang (1994) considered the problem of estimating the integral Sθ = ∫ θ dF, based on a possibly censored sample from a distribution F, where θ is an F-integrable function. They proposed a Kaplan-Meier integral to approximate Sθ and derived an explicit formula for the delete-1 jackknife estimate . differs from only when the largest observation, X(n), is not censored (δ(n) = 1 and next-to-the-largest observation, X(n-1), is censored (δ(n-1) = 0). In this note, it will pointed out that when X(n) is censored is based on a defective distribution, and therefore can badly underestimate . We derive an explicit formula for the delete-2 jackknife estimate . However, on comparing the expressions of and , their difference is negligible. To improve the performance of and , we propose a modified estimator according to Efron (1980). Simulation results demonstrate that is much less biased than and and . 相似文献
6.
Kui Liu 《Journal of Number Theory》2011,131(12):2247-2261
Let be the error term of the Riesz mean of the symmetric square L-function. We give the higher power moments of and show that if there exists a real number A0:=A0(ρ)>3 such that , then we can derive asymptotic formulas for , 3?h<A0, h∈N. Particularly, we get asymptotic formulas for , h=3,4,5 unconditionally. 相似文献
7.
Melvyn B. Nathanson 《Journal of Number Theory》2009,129(6):1608-1621
The set of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If an∼αnh for some real number α>0, then α is called an additive eigenvalue of order h. The additive spectrum of order h is the set N(h) consisting of all additive eigenvalues of order h. It is proved that there is a positive number ηh?1/h! such that N(h)=(0,ηh) or N(h)=(0,ηh]. The proof uses results about the construction of supersequences of sequences with prescribed asymptotic growth, and also about the asymptotics of rearrangements of infinite sequences. For example, it is proved that there does not exist a strictly increasing sequence of integers such that bn∼n2 and B contains a subsequence such that bnk∼k3. 相似文献
8.
Long Chen Yonggang Wang Jinbiao Wu 《Journal of Computational and Applied Mathematics》2008,220(1-2):712-724
A one-dimensional singularly perturbed problem with a boundary turning point is considered in this paper. Let Vh be the linear finite element space on a suitable grid . A variant of streamline diffusion finite element method is proved to be almost uniform stable in the sense that the numerical approximation uh satisfies u-uh∞C|lnε| infvhVhu-vh∞, where C is independent with the small diffusion coefficient ε and the mesh . Such stability result is applied to layer-adapted grids to obtain almost ε-uniform second order scheme for turning point problems. 相似文献
9.
We find a sufficient condition that is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function cannot be level if hd≤2d+3, and that there exists a level O-sequence of codimension 3 of type for hd≥2d+k for k≥4. Furthermore, we show that is not level if , and also prove that any codimension 3 Artinian graded algebra A=R/I cannot be level if . In this case, the Hilbert function of A does not have to satisfy the condition hd−1>hd=hd+1.Moreover, we show that every codimension n graded Artinian level algebra having the Weak-Lefschetz Property has a strictly unimodal Hilbert function having a growth condition on (hd−1−hd)≤(n−1)(hd−hd+1) for every d>θ where
h0<h1<<hα==hθ>>hs−1>hs.