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1.
You Ming Liu 《数学学报(英文版)》2001,17(3):501-506
Let g(x) ∈L
2(R) and ğ(ω) be the Fourier transform of g(x). Define g
mn
(x) = e
imx
g(x−2πn). In this paper we shall give a sufficient and necessary condition under which {g
mn
(x)} constitutes an orthonormal basis of L
2(R) for compactly supported g(ω) or ˘(ω).
Received March 25, 1999, Revised November 5, 1999, Accepted September 6, 2000 相似文献
2.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献
3.
Ya. G. Sinai 《Commentarii Mathematici Helvetici》1985,60(1):173-178
We consider two commuting automorphismsT
1,T
2 of the Lebesque space (M, M, μ) such thath
m,n=h(T
1
m
T
2
n
)<∞ whereh is the measure-theoretic entropy. Under additional assumptions we show the existence of the limits lim (1/m)h
m,n wherem→∞,n→∞,m/n→ω and ω is an irrational number. 相似文献
4.
Fengwei Zhong Huafei Sun Zhenning Zhang 《Bulletin of the Brazilian Mathematical Society》2008,39(1):1-10
In this paper, we consider the problem of distribution control from the viewpoint of information geometry. Different from
most existing models used in stochastic control, it is assumed that the control input directly affects the distribution of
the system output in probability sense. Here, we set up a new manifold (S), meanwhile the B-spline manifold (B) and the system output manifold (M) can be referred to as its submanifolds. We give an information geometrical algorithm which can be called as geodesic-projection
algorithm using the properties of manifold. In the geodesic step, we can obtain the geodesic equation from the initial point
V0 = (ω10, ω20, ··· , ω(n−1)0) to the specified point Vg = (ω1g, ω2g, ··· , ω(n−1)g) in B. This gives us an optimal trajectory for the points changing along in B. In the projection step, we project the sample points selected from the geodesic onto M. The coordinates of the projections in M give the trajectory of the control input u. 相似文献
5.
We study the asymptotic behaviour of the trace (the sum of the diagonal parts) τ
n
= τ
n
(ω) of a plane partition ω of the positive integer n, assuming that ω is chosen uniformly at random from the set of all such partitions. We prove that (τ
n
− c
0
n
2/3)/c
1
n
1/3 log1/2
n converges weakly, as n → ∞, to the standard normal distribution, where c
0 = ζ(2)/ [2ζ(3)]2/3, c
1 = √(1/3/) [2ζ(3)]1/3 and ζ(s) = Σ
j=1∞
j
−s
.
Partial support given by the National Science Fund of the Bulgarian Ministry of Education and Science, grant No. VU-MI-105/2005. 相似文献
6.
Andreas Fr?hlich 《Annali dell'Universita di Ferrara》2000,46(1):11-19
We consider weights of Muckenhoupt classA
q, 1<q<∞. For a bounded Lipschitz domain Ω⊂ℝn we prove a compact embedding and a Poincaré inequality in weighted Sobolev spaces. These technical tools allow us to solve
the weak Neumann problem for the Laplace equation in weighted spaces on ℝn, ℝn
+, on bounded and on exterior domains Ω with boundary of classC
1, which will yield the Helmholtz decomposition ofL
ω
q(Ω)n for general ω∈A
q. This is done by transferring the method of Simader and Sohr [4] to the weighted case. Our result generalizes a result of
Farwig and Sohr [2] where the Helmholtz decomposition ofL
ω
p(Ω)n is proved for an exterior domain and weights of Muckenhoupt class without singularities or degeneracies in a neighbourhood
of ϖΩ.
Sunto In questo lavoro consideriamo dei pesi della classe di MuckenhouptA q, 1<q<∞. Per un dominio limitato lipschitziano Ω⊂ℝn, dimostriamo una immersione compatta ed una disuguaglianza di Poincaré in spazi di Sobolev con peso. Questa tecnica ci consente di risolvere il problema debole di Neumann per l’equazione di Laplace in spazi pesati in ℝn, ℝn + in domini limitati ed in domini esterni con frontiera di classeC 1, che conduce alla decomposizione di Helmholtz diL ω q(Ω)n per un qualsiasi ω∈A q. Il risultato è ottenuto trasferendo il metodo di Simader e Sohr [4] al caso pesato. Quello qui presente estende un risultato di Farwig e Sohr [2] dove la decomposizione di Helmholtz diL ω q(Ω)n è dimostrata per domini esterni e pesi della classe di Muckenhoupt privi di singolarità in un intorno di ϖΩ.相似文献
7.
Jean-Pierre Levinski 《Israel Journal of Mathematics》1984,48(2-3):225-243
We consider various forms of the Conjecture of Chang. Part A constitutes an introduction. Donder and Koepke have shown that
if ρ is a cardinal such that ρ ≧ ω1, and (ρ++,ρ+↠(ρ+, ρ), then 0+ exists. We obtain the same conclusion in Part B starting from some other forms of the transfer hypothesis. As typical corollaries,
we get:
Theorem A.Assume that there exists cardinals λ, κ, such that λ ≧
K
+ ≧ω2 and (λ+, λ)↠(K
+,K. Then 0+ exists.
Theorem B.Assume that there exists a singularcardinal κ such that(K
+,K↠(ω1, ω0. Then 0+ exists.
Theorem C.Assume that (λ
++, λ). Then 0+ exists (also ifK=ω
0.
Remark. Here, as in the paper of Donder and Koepke, “O+ exists” is a matter of saying that the hypothesis is strictly stronger than “L(μ) exists”. Of course, the same proof could give a few more sharps overL(μ), but the interest is in expecting more cardinals, coming from a larger core model.
Theorem D.Assume that (λ
++, λ)↠(K
+, K) and thatK≧ω
1. Then 0+ exists.
Remark 2. Theorem B is, as is well-known, false if the hypothesis “κ is singular” is removed, even if we assume thatK≧ω
2, or that κ is inaccessible. We shall recall this in due place.
Comments. Theorem B and Remark 2 suggest we seek the consistency of the hypothesis of the form:K
+, K↠(ωn +1, ωn), for κ singular andn≧0. 0266 0152 V 3
The consistency of several statements of this sort—a prototype of which is (N
ω+1,N
ω)↠(ω1, ω0) —have been established, starting with an hypothesis slightly stronger than: “there exists a huge cardinal”, but much weaker
than: “there exists a 2-huge cardinal”. These results will be published in a joint paper by M. Magidor, S. Shelah, and the
author of the present paper. 相似文献
8.
Ralf-Dieter Schindler 《Israel Journal of Mathematics》1997,99(1):221-230
We use the core model for the one strong cardinal to show that the Chang Conjecture (ℵ
n+2, ℵ
n+1) ⇒ (ℵ
n+1, ℵ
n
) together with 2ℵ
n − 1 = ℵ
n
implies, for 1<n<ω, the existence of an inner model with a strong cardinal. An essential step of our proof is an application of the Gitik
Game which also admits a presentation. 相似文献
9.
Hari Bercovici 《Complex Analysis and Operator Theory》2007,1(3):335-339
Consider a domain
, and two analytic matrix-valued functions functions
. Consider also points
and positive integers n
1, n
2, . . . , n
N
. We are interested in the existence of an analytic function
such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)−1 up to order n
j
at the point ω
j
. We will see that such a function exists provided that F(ω
j
),G(ω
j
) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n
j
at ω
j
. This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in
the unit disk.
The author was partially supported by a grant from the National Science Foundation.
Received: September 8, 2006. Accepted: January 11, 2007. 相似文献
10.
We deal with (n−1)-generated modules of smooth (analytic, holomorphic) vector fieldsV=(X
1,..., Xn−1) (codimension 1 differential systems) defined locally on ℝ
n
or ℂ
n
, and extend the standard duality(X
1,..., Xn−1)↦(ω), ω=Ω(X1,...,Xn−1,.,) (Ω−a volume form) betweenV′s and 1-generated modules of differential 1-forms (Pfaffian equations)—when the generatorsX
i are linearly independent—onto substantially wider classes of codimension 1 differential systems. We prove that two codimension
1 differential systemsV and
are equivalent if and only if so are the corresponding Pfaffian equations (ω) and
provided that ω has1-division property: ωΛμ=0, μ—any 1-form ⇒ μ=fω for certain function germf. The 1-division property of ω turns out to be equivalent to the following properties ofV: (a)fX∈V, f—not a 0-divisor function germ ⇒X∈V (thedivision property); (b) (V
⊥)⊥=V; (c)V
⊥=(ω); (d) (ω)⊥=V, where ⊥ denotes the passing from a module (of vector fields or differential 1-forms) to its annihilator.
Supported by Polish KBN grant No 2 1090 91 01.
Partially supported by the fund for the promotion of research at the Technion, 100–942. 相似文献
11.
Let Γ
g, n
be the mapping class group of a compact Riemann surface of genusg withn points preserved (2−2g−n<0,g≥1,n≥0). The Torelli subgroup of Γ
g, n
has a natural weight filtration {Γg, n(m)}
m≥1. Each graded quotient gr
m
Γ
g, n
⊗ ℚ (m≥1) is a finite dimensional vector space over ℚ on which the group Sp(2g, ℚ)×S
n
naturally acts.
In this paper, we have determined the Sp(2g, ℚ)×S
n
module structure of gr
m
Γ
g, n
⊗ ℚ for 1≤m≤3. This includes a verification of an expectation by S. Morita. Also, for generalm, we have identified a certain Sp(2g, ℚ)-irreducible component of gr
m
Γ
g, n
⊗ ℚ by constructing explicitly elements in these modules. 相似文献
12.
WU Hao & LI Weigu School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(12):1670-1682
In this paper, we consider the following autonomous system of differential equations: x = Ax f(x,θ), θ = ω, where θ∈Rm, ω = (ω1,…,ωm) ∈ Rm, x ∈ Rn, A ∈ Rn×n is a constant matrix and is hyperbolic, f is a C∞ function in both variables and 2π-periodic in each component of the vector e which satisfies f = O(||x||2) as x → 0. We study the normal form of this system and prove that under some proper conditions this system can be transformed to an autonomous system: x = Ax g(x), θ = ω. Additionally, the proof of this paper naturally implies the extension of Chen's theory in the quasi-periodic case. 相似文献
13.
Saharon Shelah 《Israel Journal of Mathematics》2008,166(1):61-96
We show that, consistently, there is an ultrafilter on ω such that if N
nℓ = (P
nℓ ∪ Q
nℓ, P
nℓ, Q
nℓ, R
nℓ) (for ℓ = 1, 2, n < ω), P
nℓ ∪ Q
nℓ ⊆ ω, and are models of the canonical theory t
ind of the strong independence property, then every isomorphism from onto is a product isomorphism.
The first version of this work done in 93; First typed: May 1993.
This research was partially supported by the United States-Israel Binational Science Foundation. Publication 509 相似文献
14.
We prove that scattered Eberlein compacta of Cantor-Bendixson height at most ω + 1 are Uniform Eberlein compact spaces (ω + 1 is optimal for this result). For a set X and n ∈ ω, by σ
n
(2X) we denote the subspace of the product 2X consisting of all characteristic functions of sets of cardinality ≥ n. We give an example of an Eberlein compactum K of weight ω
ω
and of Cantor-Bendixson height 3 which cannot be embedded into any σ
n
(2X).
Research of the first author supported by NSERC of Canada. Murray Bell died on December 9, 2001.
Research of the second author supported by KBN grants 2 P03A 011 15 and 2 P03A 004 23. The main part of this research was
done while the second author was visiting the University of Manitoba in 2000. He expresses his gratitude to the Department
of Mathematics of U.M. for its hospitality. 相似文献
15.
For a domainU on a certaink-dimensional minimal submanifold ofS
n orH
n, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU k
k
ω
k
M (D)
k-1
≤Vol(∂D)
k
, where ω
k
is the volume of the unit ball ofR
k
. Also, we prove that ifD is any domain on a minimal surface inS
+
n
(orH
n, respectively), thenD satisfies an isoperimetric inequality2π A≤L
2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofH
n, then(k−1) Vol(U)≤Vol(∂U).
Supported in part by KME and GARC 相似文献
16.
Let G be a locally compact group with a weight function ω. Recently, we have shown that the Banach space L0∞ (G,1/ω) can be identified with the strong dual of L1(G, ω)equipped with some locally convex topologies τ. Here we use this duality to introduce an Arens multiplication on (L1(G, ω), τ)**, and prove that the topological center of (L1(G, ω), τ)** is (L1(G, ω); this enables us to conclude that (L1(G, ω), τ) is Arens regular if and only if G is discrete. We also give a characterization for Arens regularity of L0∞ (G, 1/ω)1.
Received: 8 March 2005 相似文献
17.
Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static
magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant
conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l
and ωPg respectively. In the case of ωe⋙ωg, the PEMFs are manifested as the EM wave beams with frequency ωe and a standing EM wave with ωg. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ωg⋙ωe, all PEMFs are expressed as the standing EM waves with frequency ωg. The resonant response occurs in two cases of ωe = 1/2 ωg andωe, = ωg only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the
BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced.
This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes
of displaying perturbed effects induced by the standing GW withh = 10-33 - 10-35 and λg = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed. 相似文献
18.
Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()α≤≤ ()
n
−ω. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour
number μ(G) of G: n− (n−ω)()
n
−ω≤μ(G)≤n−α() α.
Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002 相似文献
19.
Vladimir I. Danilov Alexander V. Karzanov Gleb A. Koshevoy 《Journal of Algebraic Combinatorics》2010,32(4):497-531
For a permutation ω∈S
n
, Leclerc and Zelevinsky in Am. Math. Soc. Transl., Ser. 2 181, 85–108 (1998) introduced the concept of an ω-chamber weakly separated collection of subsets of {1,2,…,n} and conjectured that all inclusionwise maximal collections of this sort have the same cardinality ℓ(ω)+n+1, where ℓ(ω) is the length of ω. We answer this conjecture affirmatively and present a generalization and additional results. 相似文献
20.
Antonio Leaci 《manuscripta mathematica》1992,75(1):429-441
We prove the existence of a minimizing pair for the functionalG defined for every closed setK ⊂R
2 and for every functionu ∈C
1(ω/K) by
where ω is an open set inR
2, λ, μ>0,q≥1,g ∈L
q
(ω) ∩L
p
(ω) withp>2q andH
1 is the 1-dimensional Hausdorff measure. 相似文献