共查询到20条相似文献,搜索用时 31 毫秒
1.
QIU ZhiJian School of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2008,51(1):131-142
Let G be a bounded open subset in the complex plane and let H~2(G) denote the Hardy space on G. We call a bounded simply connected domain W perfectly connected if the boundary value function of the inverse of the Riemann map from W onto the unit disk D is almost 1-1 with respect to the Lebesgue measure on D and if the Riemann map belongs to the weak-star closure of the polynomials in H~∞(W). Our main theorem states: in order that for each M∈Lat (M_z), there exist u∈H~∞(G) such that M=∨{uH~2(G)}, it is necessary and sufficient that the following hold: (1) each component of G is a perfectly connected domain; (2) the harmonic measures of the components of G are mutually singular; (3) the set of polynomials is weak-star dense in H~∞(G). Moreover, if G satisfies these conditions, then every M∈Lat (M_z) is of the form uH~2(G), where u∈H~∞(G) and the restriction of u to each of the components of G is either an inner function or zero. 相似文献
2.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2).
The online version of the original article can be found at . 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
3.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2). 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
4.
LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formω →λ(X
ω
), where X
ω
are the fibres of a regular morphismf :X →W of real algebraic sets, (ii) the functions of the formω →χ(X
ω
), where X
ω
are the fibres of a proper regular morphismf :X →W of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties
with respect to the link operator and specialization.
Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN
610/P3/94. 相似文献
5.
We construct logistic maps whose restriction to the ω-limit set of its critical point is a minimal Cantor system having a prescribed number of distinct ergodic and invariant probability
measures. In fact, we show that every metrizable Choquet simplex whose set of extreme points is compact and totally disconnected
can be realized as the set of invariant probability measures of a minimal Cantor system corresponding to the restriction of
a logistic map to the ω-limit set of its critical point. Furthermore, we show that such a logistic map f can be taken so that each such invariant measure has zero Lyapunov exponent and is an equilibrium state of f for the potential −ln |f′|. 相似文献
6.
7.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
, for certain external subspaces
of the hyperfinite dimensional Banach space
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
are isometrically isomorphic as Banach algebras.
Research of both authors supported by a grant by VEGA – Scientific Grant Agency of Slovak Republic. 相似文献
8.
Ricardo Mañé 《Bulletin of the Brazilian Mathematical Society》1993,24(1):1-11
We prove a result on the backward dynamics of a rational function nearby a point not contained in the -limit set of a recurrent critical point. As a corollary we show that a compact invariant subset of the Julia set, not containing critical or parabolic points, and not intersecting the -limit set ofrecurrent critical points, is expanding, thus extending a classical criteria of Fatou. We also prove that the boundary of a Siegel disk is always contained in the -limit set of arecurrent critical point. 相似文献
9.
We introduce a notion which is intermediate between that of taking thew*-closed convex hull of a set and taking the norm closed convex hull of this set. This notion helps to streamline the proof
(given in [FLP]) of the famous result of James in the separable case. More importantly, it leads to stronger results in the
same direction. For example:
相似文献
1. | AssumeX is separable and non-reflexive and its unit sphere is covered by a sequence of balls of radiusa<1. Then for every sequence of positive numbers tending to 0 there is anf εX*, such that ‖f‖ = 1 andf (x)≤1 −ε i , wheneverx εC i ,i=1,2,… |
2. | AssumeX is separable and non-reflexive and letT:Y →X* be a bounded linear non-surjective operator. Then there is anf εX* which does not attain its norm onB X such thatf ∉T(Y). |
10.
11.
We introduce a notion of energy for harmonic currents of bidegree (1, 1) on a complex K?hler manifold (M, ω). This allows us to define
for positive harmonic currents. We then show that for a lamination with singularities of a compact set in
without directed positive closed currents, there is a unique positive harmonic current which minimizes energy. If X is a compact laminated set in
of class
it carries a unique positive harmonic current T of mass 1. The current T can be obtained by an Ahlfors type construction starting with an arbitrary leaf of X. When X has a totally disconnected set of singularities, contained in a countable union of analytic sets, the above construction
still gives positive harmonic currents.
Received: February 2004 Revision: December 2004 Accepted: June 2005 相似文献
12.
Let X be a Banach space with the Grothendieck property, Y a reflexive Banach space, and let X ⊗̌ɛ
Y be the injective tensor product of X and Y.
(a) |
If either X** or Y has the approximation property and each continuous linear operator from X* to Y is compact, then X ⊗̌ɛ
Y has the Grothendieck property. 相似文献
13.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
14.
Pál Pusztai 《Central European Journal of Operations Research》2008,16(4):407-414
Let us suppose that X is a given, finite, not empty set and ${\mathcal F}
15.
Here we prove the following result.
Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pick
(X) with h
0
(X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h
0(X,M)=r+1≧2, h1
(X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h
0 (X, M ⊗(L*)⊗n)>0}. Then one of the following cases occur:
Sunto In questo lavoro si dimostra il seguente teorema. Teorem 1.1.Sia X una curva proiettiva ridotta e irriducibile di genere aritmetico g e k≥4 un intero. Si supponga l'esistenza di L ε Pick (X) con h 0 (X, L)=2 e L generato. Si fissi un fascio senza torsione di rango uno M su X con h0 (X, M)=r++1≥2, h1 (X, M) ≧2 e M generato dalle sue sezioni globali. Si ponga d≔deg(M) e s≔max{n≧0:h 0(X, M ⊗(L*)⊗n)>0}. Allora si verifica uno dei casi seguenti:相似文献 16.
M. Simon 《manuscripta mathematica》2000,101(1):89-114
The purpose of this paper is to construct a set of Riemannian metrics on a manifold X with the property that will develop a pinching singularity in finite time when evolved by Ricci flow. More specifically, let , where N
n
is an arbitrary closed manifold of dimension n≥ 2 which admits an Einstein metric of positive curvature. We construct a (non-empty) set of warped product metrics on the non-compact manifold X such that if , then a smooth solution , t∈[0,T) to the Ricci flow equation exists for some maximal constant T, 0<T<∞, with initial value , and
17.
José Rodríguez 《Archiv der Mathematik》2007,88(1):62-70
Let X be a weakly Lindel?f determined Banach space. We prove that the following two statements are equivalent:
18.
Michael Bildhauer 《manuscripta mathematica》2003,110(3):325-342
Suppose that f: ℝ
nN
→ℝ is a strictly convex energy density of linear growth, f(Z)=g(|Z|2) if N>1. If f satisfies an ellipticity condition of the form
19.
LeA be an automaton whose set of inputs equalsX (|X|≧2) and whose cardinality of the set of states equalsn (n≧2), and letQ be the set of all primitive words overX. ByT(A) we denote the language accepted byA. In this paper, we give the following results:
20.
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
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