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1.
Juan Antonio Cuesta-Albertos Ricardo Fraiman Thomas Ransford 《Journal of Theoretical Probability》2007,20(2):201-209
The Cramér–Wold theorem states that a Borel probability measure P on ℝ
d
is uniquely determined by its one-dimensional projections. We prove a sharp form of this result, addressing the problem of
how large a subset of these projections is really needed to determine P. We also consider extensions of our results to measures on a separable Hilbert space.
First author partially supported by the Spanish Ministerio de Ciencia y Tecnología, grant BFM2002-04430-C02-02.
Second author partially supported by Instituto de Cooperación Iberoamericana, Programa de Cooperación Interuniversitaria AL-E
2003.
Third author partially supported by grants from NSERC and the Canada research chairs program. 相似文献
2.
The Bartle–Dunford–Schwartz integral for scalar functions with respect to vector measures is characterized by means of Riemann-type
sums based on partitions of the domain into countably many measurable sets. In this setting, two natural notions of integrability
(Birkhoff integrability and Kolmogoroff integrability) turn out to be equivalent to Bartle–Dunford–Schwartz integrability.
A. Fernández, F. Mayoral and F. Naranjo were supported by MEC and FEDER (project MTM2006–11690–C02–02) and La Junta de Andalucía. J. Rodríguez was supported by MEC and FEDER (project MTM2005-08379), Fundación Séneca (project 00690/PI/04) and the Juan de la Cierva Programme (MEC and FSE). 相似文献
3.
The well-known Taikov’s refined versions of the Hardy – Littlewood – Pólya inequality for the L
2 -norms of intermediate derivatives of a function defined on the real axis are generalized to the case of powers of self-adjoint
operators in a Hilbert space. 相似文献
4.
V. L. Selivanov 《Algebra and Logic》2007,46(2):120-133
We introduce and study some natural operations on a structure of finite labeled forests, which is crucial in extending the
difference hierarchy to the case of partitions. It is shown that the corresponding quotient algebra modulo the so-called h-equivalence
is the simplest non-trivial semilattice with discrete closures. The algebra is also characterized as a free algebra in some
quasivariety. Part of the results is generalized to countable labeled forests with finite chains.
Supported by a DAAD project within the program “Ostpartnerschaften.”
__________
Translated from Algebra I Logika, Vol. 46, No. 2, pp. 217–243, March–April, 2007. 相似文献
5.
R. T. W. Martin 《Complex Analysis and Operator Theory》2011,5(2):545-577
Recently it has been shown that any regular simple symmetric operator with deficiency indices (1, 1) is unitarily equivalent
to the operator of multiplication in a reproducing kernel Hilbert space of functions on the real line with the Kramer sampling
property. This work has been motivated, in part, by potential applications to signal processing and mathematical physics.
In this paper we exploit well-known results about de Branges–Rovnyak spaces and characteristic functions of symmetric operators
to prove that any such a symmetric operator is in fact unitarily equivalent to multiplication by the independent variable
in a de Branges space of entire functions. This leads to simple new results on the spectra of such symmetric operators, on
when multiplication by z is densely defined in de Branges–Rovnyak spaces in the upper half plane, and to sufficient conditions for there to be an
isometry from a given subspace of
L2 (\mathbbR, dn){L^2 (\mathbb{R}, d\nu)} onto a de Branges space of entire functions which acts as multiplication by a measurable function. 相似文献
6.
We study Lipschitz contraction properties of general Markov kernels seen as operators on spaces of probability measures equipped
with entropy-like ``distances'. Universal quantitative bounds on the associated ergodic constants are deduced from Dobrushin's
ergodic coefficient. Strong contraction properties in Orlicz spaces for relative densities are proved under more restrictive
mixing assumptions. We also describe contraction bounds in the entropy sense around arbitrary probability measures by introducing
a suitable Dirichlet form and the corresponding modified logarithmic Sobolev constants. The interest in these bounds is illustrated
on the example of inhomogeneous Gaussian chains. In particular, the existence of an invariant measure is not required in general.
Received: 31 October 2000 / Revised version: 21 February 2003 /
Published online: 12 May 2003
L. Miclo also thanks the hospitality and support of the Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brasil,
where part of this work was done.
Mathematics Subject Classification (2000): 60J05, 60J22, 37A30, 37A25, 39A11, 39A12, 46E39, 28A33, 47D07
Key words or phrases: Lipschitz contraction – Generalized relative entropy – Markov kernel – Dobrushin's ergodic coefficient – Orlicz norm – Dirichlet
form – Spectral gap – Modified logarithmic Sobolev inequality – Inhomogeneous Gaussian chains – Loose of memory property 相似文献
7.
8.
LetE be a complex Banach space with open unit ballB
e. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onB
e with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly
insideB
e form a path connected component. WhenE is a Hilbert space or aC
o(X)- space, the path connected components are shown to be the open balls of radius 2.
The research of this author was supported by grant number SAB1999-0214 from the Ministerio de Educación, Cultura y Deporte
during his stay at the Universidad de Valencia.
The research of this author was partially supported DGES(Spain) pr. 96-0758.
The research of this author was partially supported by Magnus Ehrnrooths stiftelse. 相似文献
9.
In Macheras and Strauss (Atti Sem Math Fis Univ Modena, L, pp 349–361, 2002) and Musial et al. (J Theor Probab 20:545–560,
2007) various products for primitive liftings in the factors of a product of probability spaces have been considered. In this
paper we settle for the d-dimensional Lebesgue densities open problems from Macheras and Strauss (Atti Sem Math Fis Univ Modena, L, pp 349–361, 2002)
and Musial et al. (J Theor Probab 20:545–560, 2007) by applying results relying on the metrical group structure of
\mathbb Rd{{\mathbb R}^d}, if
d ? \mathbb N{d\in{\mathbb N}}. In particular, a lifting problem from Musial et al. (Arch Math 83:467–480, 2004), Question 3.3, is decided to the negative
for the Lebesgue densities. The relation of the Lebesgue density in the product space and the results of the products taken
for the Lebesgue densities in the factors under order is discussed. The results can be carried over to densities and liftings
dominating Lebesgue densities and to multiplicative and positive linear liftings on function spaces. 相似文献
10.
This note presents a commutant lifting theorem (CLT) with initial data a finite set of (test) functions and a compatible reproducing
kernel k on a set X. This covers the CLT of Ball, Li, Timotin, and Trent [9] for the polydisc, but in general no analyticity is required, rather
statements and proofs use the language and techniques of reproducing kernel Hilbert spaces. Uniqueness of the de Branges–Rovnyak
construction like found in Agler [1] and Ambrozie, Englis, and Müller [5] and an abstract Beurling Theorem in the present
context are of independent interest.
Received: October 12, 2006. Accepted: May 8, 2007. 相似文献
11.
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group
representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces
of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo
invariant
Members of VBAC (Vector Bundles on Algebraic Curves). Second and Third authors partially supported by Ministerio de Educación
y Ciencia and Conselho de Reitores das Universidades Portuguesas through Acción Integrada Hispano-Lusa HP2002-0017 (Spain)/E–30/03
(Portugal). First and Second authors partially supported by Ministerio de Educación y Ciencia (Spain) through Project MTM2004-07090-C03-01.
Third author partially supported by the Centro de Matemática da Universidade do Porto and the project POCTI/MAT/58549/2004,
financed by FCT (Portugal) through the programmes POCTI and POSI of the QCA III (2000–2006) with European Community (FEDER)
and national funds. The second author visited the IHES with the partial support of the European Commission through its 6th
Framework Programme “Structuring the European Research Area” and the Contract No. RITA-CT-2004-505493 for the provision of
Transnational Access implemented as Specific Support Action 相似文献
12.
Can Qin TANG Qing Guo LI Bo Lin MA 《数学学报(英文版)》2005,21(3):599-612
Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B(f, g) given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section. 相似文献
13.
This paper introduces a projection subgradient system modeled by an evolution differential inclusion to solve a class of hierarchical
optimization problems in Hilbert space. Basing on the Moreau–Yosida approximation, we prove the global existence and uniqueness
of the solution of the proposed evolution differential inclusion with projection and the unique solution of the proposed system
is just its “slow solution” when the constrained set is defined by the affine equalities. When the outer layer objective function
ψ is strongly convex, any solution of the proposed system is strongly convergent to the unique minimizer of the constrained
optimization problem, while, the strongly convergence is also given when the inner layer objective function ϕ is strongly convex. Furthermore, we present some other optimization problem models, which can be solved by the proposed system.
All the results obtained are new not only in the infinite dimensional Hilbert space framework but also in the finite dimensional
space. 相似文献
14.
In this paper, we develop the results in Rudnicki (Stoch. Process. Appl. 108:93–107, 2003) to a stochastic predator-prey system where the random factor acts on the coefficients of environment. We show that there
exists the density functions of the solutions and then, study the asymptotic behavior of these densities. It is proved that
the densities either converges in L
1 to an invariant density or converges weakly to a singular measure on the boundary. 相似文献
15.
Peter Vadovič 《Mathematica Slovaca》2008,58(4):509-520
We consider a special space of set-valued functions (multifunctions), the space of densely continuous forms D(X, Y) between Hausdorff spaces X and Y, defined in [HAMMER, S. T.—McCOY, R. A.: Spaces of densely continuous forms, Set-Valued Anal. 5 (1997), 247–266] and investigated also in [HOLá, L’.: Spaces of densely continuous forms, USCO and minimal USCO maps, Set-Valued Anal. 11 (2003), 133–151]. We show some of its properties, completing the results from the papers [HOLY, D.—VADOVIČ, P.: Densely continuous forms, pointwise topology and cardinal functions, Czechoslovak Math. J. 58(133) (2008), 79–92] and [HOLY, D.—VADOVIČ, P.: Hausdorff graph topology, proximal graph topology and the uniform topology for densely continuous forms and minimal USCO maps, Acta Math. Hungar. 116 (2007), 133–144], in particular concerning the structure of the space of real-valued locally bounded densely continuous forms
D
p
*(X) equipped with the topology of pointwise convergence in the product space of all nonempty-compact-valued multifunctions.
The paper also contains a comparison of cardinal functions on D
p
*(X) and on real-valued continuous functions C
p
(X) and a generalization of a sufficient condition for the countable cellularity of D
p
*(X).
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904 and by the Eco-Net
(EGIDE) programme of the Laboratoire de Mathématiques de l’Université de Saint-Etienne (LaMUSE), France. 相似文献
16.
In this work we analyze the paper “Brimberg, J. (1995): The Fermat-Weber location problem revisited. Mathematical Programming 71, 71–76” which claims to close the question on the conjecture posed by Chandrasekaran and Tamir in 1989 on the convergence
of the Weiszfeld algorithm. Some counterexamples are shown to the proofs showed in Brimberg’s paper.
Received: January 1999 / Accepted: December 2001?Published online April 12, 2002
RID="*"
ID="*"Partially supported by PB/11/FS/97 of Fundación Séneca of the Comunidad Autónoma de la Región de Murcia
RID="**"
ID="**"Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+I+D), project TIC2000-1750-C06-06
RID="*"
RID="**" 相似文献
17.
M. A. Mosquera I. García-Jurado M. G. Fiestras-Janeiro 《Annals of Operations Research》2008,158(1):183-188
In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies
this property.
The authors acknowledge the financial support of Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia through projects SEJ2005-07637-C02-02 and PGIDIT06PXIC207038PN. 相似文献
18.
Soit f une fonction définie sur un ouvert de ℝ
d
, à valeurs positives ou nulles, de classe C
k
, où k est un entier ≥2. Un résultat de Colombini–Jannelli–Spagnolo assure que ∇(f
1/
k
) appartient à L
1
loc. Nous démontrons ici que ∇(f
1/
k
)∈L
w
k
/
k
−2, ce qui fournit une amélioration optimale du résultat ci-dessus et une généralisation d’un théorème classique de Glaeser
sur la racine carrée. La méthode de preuve requiert l’usage d’une décomposition de Calderón–Zygmund de la fonction f qui nous permet de nous ramener à des formes normales de manipulation simple. Nous montrons également que la régularité C
k
est essentiellement nécessaire au résultat. Nous donnons quelques applications à des problèmes d’équations aux dérivées partielles
faiblement hyperboliques. L’adaptabilité des méthodes de décomposition de Calderón-Zygmund, utilisées en analyse harmonique
et pseudo-différentielle, trouve dans ces résultats une nouvelle illustration.
Received: December 13, 2001?Published online: April 14, 2003 相似文献
Received: December 13, 2001?Published online: April 14, 2003 相似文献
19.
Antonio Fernández Fernando Mayoral Francisco Naranjo Enrique A. Sánchez–Pérez 《Positivity》2009,13(1):129-143
Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L1(n) = L1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation
of the space L1(m) associated to downward directed subsets of the set of all the representations.
This research has been partially supported by La Junta de Andalucía. The support of D.G.I. under project MTM2006–11690–C02
(M.E.C. Spain) and FEDER is gratefully acknowledged. 相似文献
20.
In this paper, stochastic Volterra equations driven by cylindrical Wiener process in Hilbert space are investigated. Sufficient
conditions for existence of strong solutions are given. The key role is played by convergence of α-times resolvent families.
Both authors are supported partially by project “Proyecto Anillo: Laboratorio de Analisis Estocastico; ANESTOC”. 相似文献