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1.
Francisco Marcellán Franz Peherstorfer Robert Steinbauer 《Advances in Computational Mathematics》1997,7(3):401-428
Let
and
be polynomials orthogonal on the unit circle with respect to the measures dσ and dμ, respectively. In this paper we consider the question how the orthogonality measures dσ and dμ are related to each other if the orthogonal polynomials are connected by a relation of the form
, for
, where
. It turns out that the two measures are related by
if
, where
and
are known trigonometric polynomials of fixed degree and where the
's are the zeros of
on
. If the
's and
's are uniformly bounded then (under some additional conditions) much more can be said. Indeed, in this case the measures
dσ and dμ have to be of the form
and
, respectively, where
are nonnegative trigonometric polynomials. Finally, the question is considered to which weight functions polynomials of the
form
where
denotes the reciprocal polynomial of
, can be orthogonal.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
L. G. Rybnikov 《Functional Analysis and Its Applications》2006,40(3):188-199
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 相似文献
3.
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. 相似文献
4.
Given a positive locally finite Borel measure μ on R, a natural way to construct
multifractal wavelet series
is to set
, where
. Indeed, under suitable conditions,
it is shown that the function Fμ inherits the multifractal properties of μ.
The transposition of multifractal properties works with many classes of statistically selfsimilar
multifractal measures, enlarging the class of processes which have self-similarity properties
and controlled multifractal behaviors. Several perturbations of the wavelet coefficients and their impact on the multifractal
nature
of Fμ are studied. As an application, multifractal Gaussian processes associated with Fμ are
created. We obtain results for the multifractal spectrum of the so-called W-cascades introduced
by Arnéodo et al. 相似文献
5.
Let m and n be positive integers, and μ the M"bius function. And let S
f(m,n) be the function defined by
, where f is an arithmetical function. We show that this function has many properties like the Ramanujan sum. Firstly we study the
partial summation formula involving S
f(m,n) and taking f=μ, we obtain the Dirichlet series with the coefficients Sμ(m,n) and Sμ(m,n)d(m). Moreover we show a certain property which is analogous to the orthogonality relation of the Ramanujan sums.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Letp>q and letG=Sp(p, q). LetP=LN be the maximal parabolic subgroup ofG with Levi subgroupL≅GL
q
(ℍ)×Sp(p−q). Forsεℂ andμ a highest weight of Sp(p−q), let пs,μ be the representation ofP such that its restriction toN is trivial and
⊠T
p-q
μ
, where det
q
is the determinant character of GL
q
(ℍ) andT
p-q
μ
is the irreducible representation of Sp(p−q) with highest weightμ. LetI
p,q(s, μ) be the Harish-Chandra module of the induced representation Ind
P
G
. In this paper, we shall determine the module structure and unitarity ofI
p, q(s, μ).
Partially supported by NUS grant R-146-000-026-112. 相似文献
7.
Z. Buczolich 《Acta Mathematica Hungarica》2007,117(1-2):91-140
We construct a sequence (n
k
) such that n
k + 1 − n
k
→ ∞ and for any ergodic dynamical system (X, Σ, μ, T) and f ε L
1(μ) the averages converge to ∝
X
f
dμ for μ almost every x. Since the above sequence is of zero Banach density this disproves a conjecture of J. Rosenblatt and M. Wierdl about the
nonexistence of such sequences.
Research supported by the Hungarian National Foundation for Scientific research T049727. 相似文献
8.
Tibor Krisztin 《Periodica Mathematica Hungarica》2008,56(1):83-95
In this survey paper the delay differential equation (t) = −μx(t) + g(x(t − 1)) is considered with μ ≥ 0 and a smooth real function g satisfying g(0) = 0. It is shown that the dynamics generated by this simple-looking equation can be very rich. The dynamics is completely
understood only for a small class of nonlinearities. Open problems are formulated.
Supported in part by the Hungarian NFSR, Grant No. T049516. 相似文献
9.
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). 相似文献
10.
在线性回归模型建模中, 回归自变量选择是一个受到广泛关注、文献众多,
具有很强的理论和实际意义的问题. 回归自变量选择子集的相合性是其中一个重要问题,
如果某种自变量选择方法选择的子集在样本量趋于无穷时是相合的, 而且预测均方误差较小,
则这种方法是可取的. 利用BIC准则可以挑选相合的自变量子集, 但是在自变量个数很多时计算量过大;
适应lasso方法具有较高计算效率, 也能找到相合的自变量子集; 本文提出一种更简单的自变量选择方法,
只需要计算两次普通线性回归: 第一次进行全集回归, 得到全集的回归系数估计,
然后利用这些回归系数估计挑选子集,
然后只要在挑选的自变量子集上再进行一次普通线性回归就得到了回归结果.
考虑如下的回归模型:
其中回归系数中非零分量下标的集合为,
设是本文方法选择的自变量子集下标集合,
是本文方法估计的回归系数(未选中的自变量对应的系数为零),
本文证明了, 在适当条件下,
其中表示的
分量下标在中的元素的组成的向量, 是误差方差, 是与
矩阵极限有关的矩阵和常数.
数值模拟结果表明本文方法具有很好的中小样本性质. 相似文献
11.
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.
相似文献
12.
13.
记μ为上的非负Radon测度,且仅满足对固定的C0>0和n∈(0,d],及所有的和r>0, μ(B(x,r))≤C0 rn.作者建立了一类核函数满足Hörmander条件的Marcinkiewicz积分与Lipβ(μ)(0<β)函数生成的交换子由Lp(μ)到Lq(μ),由Lp(μ) 到Lipβ-n/p(μ)及Ln/β(μ)到RBMO(μ)有界.部分结论对经典 Marcinkiewicz积分也是新的.
相似文献
14.
在本文中, 我们主要讨论了广义Cox模型的信息流扩大问题.
假设在市场中有两类投资者, 第一类投资者拥有市场信息,
这里由一个维的布朗运动和一个可积随机
测度驱动; 而第二类投资者具有扩大的信息流,
这里假设是由信息流和广义Cox的模型刻画的违约信息流生成.
我们建立和刻画了广义Cox模型并且求给出它的主要性质包括生存过程和违约条件密度.
与Cox模型显著区别的是, 如果违约由广义Cox模型模型刻画, 与Cox模型平凡的结果不同的是,
鞅的分解更复杂和具有一般性. 相似文献
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