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Revista Matemática Complutense Nº 21

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 21
Fecha de Publicación: 2008/2

Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid   

Vol 21  Nº 2   (2008)

Más información/Texto completo en  http://revistas.ucm.es/portal/ ....


1.  Contenidos / Contents  

Entropy-Expansiveness and Domination for Surface Diffeomorphisms    
PACIFICO, María José | VIEITEZ, José L.
Palabras Clave: Entropy-expansiveness; Homoclinic classes; Dominated splitting; Homoclinic tangency; Symbolic extension
Let f : M → M be a Cr-diffeomorphism, r ≥ 1, deffined on a closed manifold M. We prove that if M is a surface and K ⊂ M is a compact invariant set such that TKM = E ⊕ F is a dominated splitting then f/K is entropy expansive. Moreover C¹ generically in any dimension, isolated homoclinic classes H(p), p hyperbolic, are entropy expansive. Conversely, if there exists a C1 neighborhood U of a surface diffeomorphism f and a homoclinic class H(p), p hyperbolic, such that for every g ∈ U the continuation H(pg) of H(p) is entropy-expansive then there is a dominated splitting for f/H(p).
On the Distribution of the Power Generator over a Residue Ring for Parts of the Period     
Palabras Clave: Sequences; Pseudorandom numbers; Discrepancy; Exponential sums
This paper studies the distribution of the power generator of pseudorandom numbers over a residue ring for parts of the period. These results compliment some recently obtained distribution bounds of the power generator modulo an arbitrary number for the entire period. Also, the arbitrary modulus case may have some cryptography related applications and could be of interest in other settings which require quality pseudorandom numbers.
Note on Coupled Linear Systems Related to Two Soliton Collision for the Quartic gKdV Equation    
MARTEL, Yvan | MERLE, Frank
Palabras Clave: Soliton; Collision; gKdV equation
We consider linear systems related to the description of the collision of two solitons for the gKdV equation with quartic nonlinearity. The computations presented in this note are applied in Martel and Merle [10] to prove a result concerning inelastic (but almost elastic) collision for a nonintegrable equation.
Rigorous Numerics for the Cahn-Hilliard Equation on the Unit Square     
MAIER-PAAPE, Stanislaus | MILLER, Ulrich | MISCHAIKOW, Konstantin | WANNER, Thomas
Palabras Clave: Cahn-Hilliard equation; Stationary solutions; Bifurcation diagram; Continuation
While the structure of the set of stationary solutions of the Cahn-Hilliard equation on one-dimensional domains is completely understood, only partial results are available for two-dimensional base domains. In this paper, we demonstrate how rigorous computational techniques can be employed to establish computerassisted existence proofs for equilibria of the Cahn-Hilliard equation on the unit square. Our method is based on results by Mischaikow and Zgliczy´nski [22], and combines rigorous computations with Conley index techniques. We are able to establish branches of equilibria and, under more restrictive conditions, even the local uniqueness of specific equilibrium solutions. Sample computations for several branches are presented, which illustrate the resulting patterns.
Divergent Cesàro Means of Jacobi-Sobolev Expansions     
Palabras Clave: Jacobi-Sobolev type polynomials; Fourier expansion; Cesàro mean
Let µ be the Jacobi measure supported on the interval [­1; 1]. Let introduce the Sobolev-type inner product …. In this paper we prove that, for certain indices δ, there are functions whose Ces_aro means of order δ in the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product are divergent almost everywhere on [-1; 1].
Strongly Invertible Knots, Rational-Fold Branched Coverings, and Hyperbolic Spatial Graphs    
ICHIHARA, Kazuhiro | USHIJIMA, Akira
Palabras Clave: Spatial graph; Theta-curve; Strongly invertible knot; Simple knot; Hyperbolic manifold
A construction of a spatial graph from a strongly invertible knot was developed by the second author, and a necessary and sufficient condition for the given spatial graph to be hyperbolic was provided as well. The condition is improved in this paper. This enable us to show that certain classes of knots can yield hyperbolic spatial graphs via the construction.
A General Hilbert Space Approach to Framelets     
MICHEL, Dominik
Palabras Clave: Hilbert space; Wavelets; Multiscale approximation; Frames; Stability; Constructive
In arbitrary separable Hilbert spaces it is possible to deffine multiscale methods of constructive approximation based on product kernels, restricting their choice in certain ways. These wavelet techniques have already filtering and localization properties and they are applicable in many areas due to their generalized deffinition. But they lack detailed information about their stability and redundancy, which are frame properties. So in this work frame conditions are introduced for approximation methods based on product kernels. In order to provide stability and redundancy the choice of product kernel ansatz function has to be restricted. Taking into account the kernel conditions for multiscale and for frame approximations one is able to deffine wavelet frames (= framelets), inheriting the approximation properties of both techniques and providing a more precise tool for multiscale analysis than the normal wavelets.
Weighted Composition Operators between Weighted Bergman Spaces and Weighted Banach Spaces of Holomorphic Functions    
WOLF, Elke
Palabras Clave: Weighted Bergman space; Weighted composition operator; Weighted Banach space of holomorphic functions
We characterize boundedness and compactness of weighted composition operators acting between weighted Bergman spaces Aw;p and weighted Banach spaces H1v of holomorphic functions.
A Note on Weighted Estimates for the Schrödinger Operator   
BARCELÓ, Juan A. | BENNETT, Jonathan M. | CARBERY, Anthony | RUIZ, Alberto | VILELA, M. Cruz
Palabras Clave: Restriction theorem; Schrödinger operator
We study two problems closely related to each other. The first one is concerned with some smoothing weighted estimates with weights in a certain Morrey- Campanato spaces, for the solution of the free Schrödinger equation. The second one is a weighed trace inequality.
Toeplitz C*-Algebras on Super-Cartan Domains     
LOAIZA, Maribel | UPMEIER, Harald
Palabras Clave: Toeplitz operator algebras; Grassmann variables; Supersymmetry; Berezin quantization; Cartan domains; Vector-valued Bergman spaces
We study Hilbert spaces of super-holomorphic functions (including anti-commuting Grassmann variables) in the setting of bounded symmetric domains, more precisely for the matrix ball of arbitrary size. Our main results concern the classi cation of irreducible representations of the associated Toeplitz C*- algebra and an explicit decomposition of the super-Bergman space as a direct sum of vector-valued (ordinary) Bergman spaces.
Maximal Function Estimates for the Parabolic Mean Value Kernel    
AIMAR, Hugo | GÓMEZ, Ivana | IAFFEI, Bibiana
Palabras Clave: One-sided parabolic maximal function; Heat equation; Mean value formula
We obtain parabolic and one-sided maximal function estimates for nonisotropic dilations of the mean value kernel for the heat equation ......
Cofibrations and Bicofibrations for C*-Algebras     
POP, Ioan | TOFAN, Alina
Palabras Clave: C*-algebra; homotopic *-homomorphisms; Cofibration (bicofibration) of C*-algebras; Mapping cylinder (cone); Double mapping cylinder; Cerin's omotopy
The paper deals with the correlated concepts of cofibration and bicofibration in C*-algebra theory. We study co brations of C*-algebras introduced by Claude Schochet in [9] (see also [7]). Cofibrations are characterized by means of the mapping cylinder C*-algebras. We also de ne and analyse the notion of bicofibration for C*-algebras based on the topological model from [8] (see also [5]). As an application, an exact sequence of Cerin's homotopy groups [1] is obtained.
Tempered Radon Measures     
Palabras Clave: Radon measure; Tempered distributions; Besov spaces
A tempered Radon measure is a σ-finite Radon measure in Rn which generates a tempered distribution. We prove the following assertions. A Radon measure μ is tempered if, and only if, there is a real number βsuch that ……. finite. A Radon measure is finite if, and only if, it belongs to the positive cone…….. (equivalent norms).

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