If the integer translates of a function ø with compact support generate a frame for a subspace W of L2(?),then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. Considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. Extending work by Ben-Artzi and Ron, we characterize the existence of oblique duals generated by a function with support on an interval of length one. If such a generator exists, we show that it can be chosen with desired smoothness. Regardless whether ø is polynomial or not, the same condition implies that a polynomial dual supported on an interval of length one exists. 相似文献
This paper investigates weighted approximations for Studentized U-statistics type processes, both with symmetric and antisymmetric kernels, only under the assumption that the distribution of the projection variate is in the domain of attraction of the normal law. The classical second moment condition E|h(X1, X2)|2 < ∞ is also relaxed in both cases. The results can be used for testing the null assumption of having a random sample versus the alternative that there is a change in distribution in the sequence. 相似文献
Suppose that p = (p1, p2, …, pN) and q = (q1, q2, …, qN) are two configurations in
, which are centers of balls Bd(pi, ri) and Bd(qi, ri) of radius ri, for i = 1, …, N. In [9] it was conjectured that if the pairwise distances between ball centers p are contracted in going to the centers q,
then the volume of the union of the balls does not increase. For d = 2 this was proved in [1], and for the case when the centers are contracted continuously for all d in [2]. One extension
of the Kneser-Poulsen conjecture, suggested in [6], was to consider various Boolean expressions in the unions and intersections
of the balls, called flowers, where appropriate pairs of centers are only permitted to increase, and others are only permitted
to decrease. Again under these distance constraints, the volume of the flower was conjectured to change in a monotone way.
Here we show that these generalized Kneser-Poulsen flower conjectures are equivalent to an inequality between certain integrals
of functions (called flower weight functions) over
, where the functions in question are constructed from maximum and minimum operations applied to functions each being radially
symmetric monotone decreasing and integrable.
Research supported in part by NSF Grant No. DMS-0209595. 相似文献
The weighted Lp-spaces of entire analytic functions are generalized to the vector-valued setting. In particular, it is shown that the dual
of the space is isomorphic to when the function χK is an Lp,ρ (E)-Fourier multiplier. This result allows us to give some new characterizations of the so-called UMD-property and to represent
several ultradistribution spaces by means of spaces of vector sequences.
J. Motos is partially supported by DGI (Spain), Grant BFM 2002-04013 and Grant MTEM 2005-08350-C03-03. 相似文献
The weak convergence of the empirical process and partial sum process of the residuals from a stationary ARCH-M model is studied.
It is obtained for and
consistent estimate of the ARCH-M parameters. We find that the limiting Gaussian processes are no longer distribution free
and hence residuals cannot be treated as i.i.d. In fact the limiting Gaussian process for the empirical process is a standard
Brownian bridge plus an additional term, while the one for partial sum process is a standard Brownian motion plus an additional
term. In the special case of a standard ARCH process, that is an ARCH process with no drift, the additional term disappears.
We also study a sub-sampling technique which yields the limiting Gaussian processes for the empirical process and partial
sum process as a standard Brownian bridge and a standard Brownian motion respectively. 相似文献
LetJ denote the Bessel function of order . For >–1, the system x–/2–1/2J+2n+1(x1/2, n=0, 1, 2,..., is orthogonal onL2((0, ),xdx). In this paper we study the mean convergence of Fourier series with respect to this system for functions whose Hankel transform is supported on [0, 1].Communicated by Mourad Ismail. 相似文献
In this article, mixture distributions and weighted likelihoods are derived within an information-theoretic framework and
shown to be closely related. This surprising relationship obtains in spite of the arithmetic form of the former and the geometric
form of the latter. Mixture distributions are shown to be optima that minimize the entropy loss under certain constraints.
The same framework implies the weighted likelihood when the distributions in the mixture are unknown and information from
independent samples generated by them have to be used instead. Thus the likelihood weights trade bias for precision and yield
inferential procedures such as estimates that can be more reliable than their classical counterparts. 相似文献
Ahlswede, Khachatrian, Mauduit and A. Sárközy introduced the notion of family-complexity of families of binary sequences. They estimated the family-complexity of a large family related to Legendre symbol introduced by Goubin, Mauduit and Sárközy. Here their result is improved, and apart from the constant factor the best lower bound is given for the family-complexity. 相似文献
Let D be a quaternion division algebra with an involution of the second kind. We show that the quotient group SU(1,D)/[U(1,D),U(1,D)]
is nontrivial in general. For global fields, we completely determine this group.
Received: 11 May 2007, Revised: 15 December 2007 相似文献
In this paper we construct an almost periodic solution to a quasilinear system with constant and linear delays. We prove the asymptotic stability of this solution. 相似文献
Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω1(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω1(P) ≦ Z(P) and NG(Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result.
This paper was partly supported by Hungarian National Foundation for Scientific Research Grant # T049841 and T038059. 相似文献
Let X1 and X2 be subspaces of quotients of R
OH and C
OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor
product into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our
result produces a completely isomorphic embedding of (equipped with its natural operator space structure) into with a QWEP von Neumann algebra.
Received: June 2006, Revision: June 2007, Accepted: September 2007 相似文献
We introduce a new class of sequences called NBVS to generalize GBVS, essentially extending monotonicity from “one sided”
to “two sided”, while some important classical results keep true.
Supported in part by Natural Science Foundation of China under grant number 10471130. 相似文献
We give a complete classification of -invariant real hypersurfaces in complex two-plane Grassmannians G2(Cm+2) with commuting normal Jacobi operator .
The first author was supported by MCYT-FEDER grant BFM 2001-2871-C04-01, the second author by grant Proj. No. KRF-2006-351-C00004
from Korea Research Foundation and the third author by grant Proj. No. R14-2002-003-01001-0 from Korea Research Foundation,
Korea 2006 and Proj. No. R17-2007-006-01000-0 from KOSEF. 相似文献
The paper is concerned with bounds for integrals of the type
, involving Jacobi polynomials pn(α,β) and Jacobi weights w(a,b) depending on α,β, a, b > −1, where the subsets Uk(x) ⊂ [−1, 1] located around x and are given by with . The functions to be integrated will also be of the type on the domain [−1,1] t/ Uk(x). This approach uses estimates of Jacobi polynomials modified Jacobi weights initiated by Totik and Lubinsky in [1]. Various
bounds for integrals involving Jacobi weights will be derived. The results of the present paper form the basis of the proof
of the uniform boundedness of (C, 1) means of Jacobi expansions in weighted sup norms in [3].
相似文献
We characterize all the central topological groupsG for which the centreZ(L1(G)) of the group algebra admits a finite universal Korovkin set. It is proved thatZ(L1(G)) has a finite universal Korovkin set iffĜ is a finite dimensional, separable metric space. This is equivalent to the fact thatG is separable, metrizable andG/K has finite torsion free rank, whereK is a compact open normal subgroup of certain direct summand ofG. 相似文献
We discuss a hypothetical correspondence between holonomic -modules on an algebraic variety X defined over a field of zero characteristic, and certain families of Lagrangian subvarieties in the cotangent bundle to X. The correspondence is based on the reduction to positive characteristic.
This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5,
2008. 相似文献
An elementary proof of the (known) fact that each element of the Banach spaceℓwp
(X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓwp
(X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications
to spaces of compact operators on Banach sequence spaces are considered. 相似文献