共查询到20条相似文献,搜索用时 46 毫秒
1.
Li Hui Peng 《Numerical Functional Analysis & Optimization》2013,34(3):284-300
The notion of superframe in general Hilbert spaces was introduced in the context of multiplexing, which has been widely used in mobile communication network, satellite communication network and computer area network. The notion of oblique dual frame is a generalization of conventional dual frame. It has provided us with a frame-like expansion. Using oblique dual frames one can extend frame expansions to include redundant expansions in which the analysis and synthesis frames lie in different spaces. Given positive integers L, M and N, an N?-periodic set 𝕊 in ?, let 𝒢(g, N, M) be a frame for l 2(𝕊, ? L ), and let 𝒢(h, N, M) be a frame for ?(h, N, M) (generated by 𝒢(h, N, M)). This article addresses super Gabor duals of g in ?(h, N, M). We obtain a necessary and sufficient condition on h admitting super oblique Gabor duals of g, and present a parametrization expression of all super oblique Gabor duals and all oblique canonical Gabor duals of g. We also characterize the uniqueness of super oblique Gabor dual and oblique canonical Gabor dual of g. Some examples are also provided. 相似文献
2.
Deguang Han 《Journal of Fourier Analysis and Applications》2009,15(2):201-217
Let
be a full rank time-frequency lattice in ℝ
d
×ℝ
d
. In this note we first prove that any dual Gabor frame pair for a Λ-shift invariant subspace M can be dilated to a dual Gabor frame pair for the whole space L
2(ℝ
d
) when the volume v(Λ) of the lattice Λ satisfies the condition v(Λ)≤1, and to a dual Gabor Riesz basis pair for a Λ-shift
invariant subspace containing M when v(Λ)>1. This generalizes the dilation result in Gabardo and Han (J. Fourier Anal. Appl. 7:419–433, [2001]) to both higher dimensions and dual subspace Gabor frame pairs. Secondly, for any fixed positive integer N, we investigate the problem whether any Bessel–Gabor family G(g,Λ) can be completed to a tight Gabor (multi-)frame G(g,Λ)∪(∪
j=1
N
G(g
j
,Λ)) for L
2(ℝ
d
). We show that this is true whenever v(Λ)≤N. In particular, when v(Λ)≤1, any Bessel–Gabor system is a subset of a tight Gabor frame G(g,Λ)∪G(h,Λ) for L
2(ℝ
d
). Related results for affine systems are also discussed.
Communicated by Chris Heil. 相似文献
3.
Consider the standard non-linear regression model y
i
= g(x
i
, θ
0)+ε
i
, i = 1, ... ,n where g(x, θ) is a continuous function on a bounded closed region X × Θ, θ
0 is the unknown parameter vector in Θ ⊂ R
p
, {x
1, x
2, ... , x
n
} is a deterministic design of experiment and {ε1, ε2, ... , ε
n
} is a
sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result
is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995)
(J. of Multivariate Analysis, vol. 54, pp. 227–238, Corrigenda. vol. 55, p. 350) is not correct.
This research was supported by the Natural Science Foundation of China (Grant No. 19831010 and grant No. 39930160) and the
Doctoral Foundation of China 相似文献
4.
Michel Talagrand 《Probability Theory and Related Fields》2001,121(2):237-268
We study the Hopfield model at temperature 1, when thenumber M(N) of patterns grows a bit slower than N. We reach a goodunderstanding of the model whenever M(N)≤N/(log N)11. For example, we show that if M(N)→∞, for two typical configurations σ
1, σ
2, (∑
i
≤
N
σ1
i
σ2
i
)2 is close to NM(N).
Received: 15 December 1999 / Revised version: 8 December 2000 / Published online: 23 August 2001 相似文献
5.
Let X be an infinite-dimensional Banach space with weight τ. By Cld
AW
(X), we denote the hyperspace of nonempty closed sets in X with the Attouch—Wets topology. By Fin
AW
(X), Comp
AW
(X) and Bdd
AW
(X), we denote the subspaces of Cld
AW
(X) consisting of finite sets, compact sets and bounded closed sets, respectively. In this paper, it is proved that
Fin
AW
(X)≈Comp
AW
(X)≈ℓ2(τ)×ℓ2
f
ℓandℓBdd
AW
(X)≈ℓ2(2τ)×ℓ2
f
where ≈ means ‘is homeomorphic to’, ℓ2(τ) is the Hilbert space with weight τ (ℓ2(ℵ0)=ℓ2 the separable Hilbert space) and
ℓ2
f
={(x
i
)
iεN
εℓ2∣x
i
=0 except for finitely many iεN}. 相似文献
6.
Michel Talagrand 《Israel Journal of Mathematics》1992,79(2-3):207-224
Consider a setA of symmetricn×n matricesa=(a
i,j)
i,j≤n
. Consider an independent sequence (g
i)
i≤n
of standard normal random variables, and letM=Esupa∈A|Σi,j⪯nai,jgigj|. Denote byN
2(A, α) (resp.N
t(A, α)) the smallest number of balls of radiusα for thel
2 norm ofR
n
2 (resp. the operator norm) needed to coverA. Then for a universal constantK we haveα(logN
2(A, α))1/4≤KM. This inequality is best possible. We also show that forδ≥0, there exists a constantK(δ) such thatα(logN
t≤K(δ)M.
Work partially supported by an N.S.F. grant. 相似文献
7.
Ronald DeVore Guergana Petrova Przemyslaw Wojtaszczyk 《Constructive Approximation》2011,33(1):125-143
Let f be a continuous function defined on Ω:=[0,1]
N
which depends on only ℓ coordinate variables, f(x1,?,xN)=g(xi1,?,xil)f(x_{1},\ldots,x_{N})=g(x_{i_{1}},\ldots,x_{i_{\ell}}). We assume that we are given m and are allowed to ask for the values of f at m points in Ω. If g is in Lip1 and the coordinates i
1,…,i
ℓ
are known to us, then by asking for the values of f at m=L
ℓ
uniformly spaced points, we could recover f to the accuracy |g|Lip1
L
−1 in the norm of C(Ω). This paper studies whether we can obtain similar results when the coordinates i
1,…,i
ℓ
are not known to us. A prototypical result of this paper is that by asking for C(ℓ)L
ℓ
(log 2
N) adaptively chosen point values of f, we can recover f in the uniform norm to accuracy |g|Lip1
L
−1 when g∈Lip1. Similar results are proven for more general smoothness conditions on g. Results are also proven under the assumption that f can be approximated to some tolerance ε (which is not known) by functions of ℓ variables. 相似文献
8.
For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N+X=M with M/X singular, we have X=M. Let ℘ be the class of all singular simple modules. Then δ(M)=Σ{ L≤ M| L is a δ-small submodule of M} = Re
jm(℘)=∩{ N⊂ M: M/N∈℘. We call M δ-coatomic module whenever N≤ M and M/N=δ(M/N) then M/N=0. And R is called right (left) δ-coatomic ring if the right (left) R-module R
R(RR) is δ-coatomic. In this note, we study δ-coatomic modules and ring. We prove M=⊕
i=1
n
Mi is δ-coatomic if and only if each M
i (i=1,…, n) is δ-coatomic. 相似文献
9.
Let M(N) be a sequence of integers with M→∞ as N→∞ and M=o(N). For bounded i.i.d. r.v. ξ
i
k
and bounded i.i.d. r.v. σ
i
, we study the large deviation of the family of (ordered) scalar products X
k
=N
−1∑
i
=1
N
σ
i
ξ
i
k
,k≤M, under the distribution conditioned on the ξ
i
k
's. To get a full large deviation principle, it is necessary to specify also the total norm(∑
k
≤
M
(X
k
)2)1/2, which turns to be associated with some extra Gaussian distribution. Our results apply to disordered, mean-field systems,
including generalized Hopfield models in the regime of a sublinear number of patterns. We build also a class of examples where
this norm is the crucial order parameter.
Received: 6 April 1999 / Revised version: 29 May 2000 /?Published online: 24 July 2001 相似文献
10.
For a stochastically continuous stochastic process with independent increments overD[0,T], letN(t,ε) be the number of smaple function jumps that occur in the interval [0,t] of sizes less than −ε or greater than ε, where ε>0. LetM(t,ε)=EN(t,ε), and assumeM(t,0+)=∞ for 0<t≦T. If limε
↓0(M(t,ε)/M(T,ε)) exists and is positive for eacht∈(0,T], then limε
↓0(N(t,ε)/M(T,ε)) for allt∈(0,T] with probability one.
The research of Howard G. Tucker was supported in part by the National Science Foundation, Grant No. MCS76-03591A01. 相似文献
11.
Ole Christensen Hong Oh Kim Rae Young Kim 《Journal of Fourier Analysis and Applications》2011,17(4):640-655
The R-dual sequences of a frame {f
i
}
i∈I
, introduced by Casazza, Kutyniok and Lammers in (J. Fourier Anal. Appl. 10(4):383–408, 2004), provide a powerful tool in the analysis of duality relations in general frame theory. In this paper we derive conditions
for a sequence {ω
j
}
j∈I
to be an R-dual of a given frame {f
i
}
i∈I
. In particular we show that the R-duals {ω
j
}
j∈I
can be characterized in terms of frame properties of an associated sequence {n
i
}
i∈I
. We also derive the duality results obtained for tight Gabor frames in (Casazza et al. in J. Fourier Anal. Appl. 10(4):383–408,
2004) as a special case of a general statement for R-duals of frames in Hilbert spaces. Finally we consider a relaxation of the
R-dual setup of independent interest. Several examples illustrate the results. 相似文献
12.
LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup
N
‖Σ
j
=0N
T
j
g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles
are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed. 相似文献
13.
In this paper, we focus our attention on the precise asymptotics of error variance estimator in partially linear regression
models, y
i
= x
i
τ
β + g(t
i
) + ε
i
, 1 ≤ i ≤ n, {ε
i
, i = 1, ⋯ n} are i.i.d random errors with mean 0 and positive finite variance σ
2. Following the ideas of Allan Gut and Aurel Spătaru[7,8] and Zhang[21], on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm,
respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.
相似文献
14.
Basic facts for Gabor frame {Eu(m)bTu(n)ag}m,n∈p on local field are investigated. Accurately, that the canonical dual of frame {Eu(m)bTu(n)ag}m,n∈p also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu(m)bTu(n)ag}m,n∈p to be a frame for L2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L2(K) are established. An example is finally given. 相似文献
15.
Banach frames and atomic decompositions are sequences that have basis-like properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove several functional — analytic properties of these decompositions, and show how these properties apply to Gabor and wavelet systems. We first prove that frames and atomic decompositions are stable under small perturbations. This is inspired by corresponding classical perturbation results for bases, including the Paley — Wiener basis stability criteria and the perturbation theorem el kato. We introduce new and weaker conditions which ensure the desired stability. We then prove quality properties of atomic decompositions and consider some consequences for Hilbert frames. Finally, we demonstrate how our results apply in the practical case of Gabor systems in weighted L2 spaces. Such systems can form atomic decompositions for L2w(IR), but cannot form Hilbert frames but L2w(IR) unless the weight is trivial. 相似文献
16.
LetM
ℛ f be the Kakeya maximal function in d-dimensional Euclidean space with some base ℛ, consisting of cylinders of eccentricity
N. The inequality ∥M
ℛ
f∥
d
⩽c(logN)ε∥ is shown for a base ℛ satisfying a direction condition, where ε and c are constants depending only on d.
to the memory of Professor Ruilin Long
The author is partly supported by the Grants-in-Aid for Scientific Research, The Ministry of Education, Science and Culture,
Japan. 相似文献
17.
We consider a parabolic semilinear problem with rapidly oscillating coefficients in a domain Ωε that is ε-periodically perforated by small holes of size O\mathcal {O}(ε). The holes are divided into two ε-periodical sets depending on the boundary interaction at their surfaces, and two different
nonlinear Robin boundary conditions σε(u
ε) + εκ
m
(u
ε) = εg
(m)
ε, m = 1, 2, are imposed on the boundaries of holes. We study the asymptotics as ε → 0 and establish a convergence theorem without
using extension operators. An asymptotic approximation of the solution and the corresponding error estimate are also obtained.
Bibliography: 60 titles. Illustrations: 1 figure. 相似文献
18.
We prove that the number of elliptic curves E/ℚ with conductorN isO(N
1/2+ε). More generally, we prove that the number of elliptic curves E/ℚ with good reduction outsideS isO(M
1/2+ε), whereM is the product of the primes inS. Assuming various standard conjectures, we show that this bound can be improved toO(M
c/loglogM
).
Research partially supported by NSF DMS-9424642. 相似文献
19.
Sambaiah Kilaru 《Proceedings Mathematical Sciences》1998,108(3):217-226
We identify the spaces Homi(ℙ1,M) fori = 1, 2, whereM is the moduli space of vector bundles of rank 2 and determinant isomorphic to
,x
0 ∈X, on a compact Riemann surface of genusg ≥ 2. 相似文献
20.
WangShiying ZhangYuren LiuYan 《高校应用数学学报(英文版)》1999,14(4):492-494
Abstract. Let Sn be the symmetric group 相似文献