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Revista Matemática Complutense Nº 17

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 17
Fecha de Publicación: 2004/2

Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid

Vol 17  Nº 2   (2004)

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


A Symmetrization Result for Nonlinear Elliptic Equations  
FERONE, Vicenzo | MESSANO, Basilio

Palabras Clave: symmetrization, rearrangement, nonlinear elliptic PDE’s
We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x, u) + f, where the principal term is a Leray-Lions operator defined onW1,p. 


Principe d’incertitude qualitatif pour les groupes de Lie nilpotents  
BOUALI, Bouchta | HEMDAOUI, Mohammed

Palabras Clave: nilpotent Lie groups, representations, orbit method.
We prove that any simply connected nilpotent Lie group satisfies the qualitative uncertainty principle. 


Active Sums I  
DÍAZ-BARRIGA, Alejandro J. | GONZÁLEZ-ACUÑA, Francisco | MARMOLEJO, Francisco | ROMÁN, Leopoldo

Palabras Clave: active sums, active sums of cyclic groups, regularity and independence, atomic and molecular groups.
Given a generating family F of subgroups of a group G, closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ' G/Z(G), where Z denotes the center. The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the group G? The conditions found to answer this question are often of a homological nature. We show that the following groups are active sums of cyclic subgroups: free groups, semidirect products of cyclic groups, Coxeter groups, Wirtinger approximations, groups of order p3 with p an odd prime, simple groups with trivial Schur multiplier, and special linear groups SLn(q) with a few exceptions. We show as well that every finite group G such that G/G0 is not cyclic is the active sum of proper normal subgroups. 


Functional Calculus in Weighted Group Algebras    

Palabras Clave: weight, weighted group algebra, functional calculus, Wiener property
Let G be a compactly generated, locally compact group with polynomial growth and let ! be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G, !). This functional calculus is then used to study harmonic analysis properties of L1(G, !), such as the Wiener property and Domar’s theorem. 


Existence Results for Quasilinear Degenerated Equations Via Strong Convergence of Truncations  
AKDIM, Youssef | AZROUL, Elhoussine | BENKIRANE, Abdelmoujib

Palabras Clave: Weighted Sobolev spaces, Hardy inequality, Quasilinear degenerated elliptic operators, Truncations
In this paper we study the existence of solutions for quasilinear degenerated elliptic operators A(u) + g(x, u,ru) = f , where A is a Leray-Lions operator from W1,p 


Constructible Functions on 2-dimensional Analytic Manifolds  
BONNARD, Isabelle | PIERONI, Federica

Palabras Clave: global semianalytic sets, constructible functions.
We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibres of proper analytic morphisms, to be such a sum of signs. 


Real Cubic Hypersurfaces and Group Laws  
HUISMAN, Johannes

Palabras Clave: real cubic hypersurface, real cubic curve, real cubic surface, pseudohyperplane, pseudo-line, pseudo-plane, linear subspace, group.
Let X be a real cubic hypersurface in Pn. Let C be the pseudo-hyperplane of X, i.e., C is the irreducible global real analytic branch of the real analytic variety X(R) such that the homology class [C] is nonzero in Hn−1(Pn(R), Z/2Z). Let L be the set of real linear subspaces L of Pn of dimension n − 2 contained in X such that L(R) _ C. We show that, under certain conditions on X, there is a group law on the set L. It is determined by L + L0 + L00 = 0 in L if and only if there is a real hyperplane H in Pn such that H • X = L + L0 + L00. We also study the case when these conditions on X are not satisfied. 


On the L2-pointwise Regularity of Functions in Critical Besov Spaces  
MOUSSA, Mohamed

Palabras Clave: Besov spaces, Calder´on-Zygmund classes, critical indexes, Haussdorff dimension, multifractal functions
We show that the functions in L2(Rn) given by the sum of infinitely sparse wavelet expansions are regular, i.e. belong to C1L2 (x0), for all x0 2 Rn which is outside a set of vanishing Hausdorff dimension. 


Approximation of Holomorphic Mappings on Infinite Dimensional Spaces  

Palabras Clave: Holomorphic mappings; holomorphic mappings of bounded type; approximation property; compact approximation property.
In this article we examine necessary and sufficient conditions for the predual of the space of holomorphic mappings of bounded type, Gb(U), to have the approximation property and the compact approximation property and we consider when the predual of the space of holomorphic mappings, G(U), has the compact approximation property. We obtain also similar results for the preduals of spaces of m-homogeneous polynomials, Q(mE). 


Dotted Links, Heegaard Diagrams, and Colored Graphs for PL 4-manifolds  
CASALI, María Rita

Palabras Clave: PL-manifold, handle-decomposition, dotted framed link, crystallization.
The present paper is devoted to establish a connection between the 4-manifold representation method by dotted framed links (or—in the closed case—by Heegaard diagrams) and the so called crystallization theory, which visualizes general PL-manifolds by means of edge-colored graphs. In particular, it is possible to obtain a crystallization of a closed 4-manifold M4 starting from a Heegaard diagram (#m(S1×S2), !), and the algorithmicity of the whole process depends on the effective possibility of recognizing (#m(S1×S2), !) to be a Heegaard diagram by crystallization theory. 


Stabilizers for Nondegenerate Matrices of Boundary Format and Steiner Bundles   

Palabras Clave: Vector bundles, multidimensional matrices, theory of invariants
In this paper nondegenerate multidimensional matrices of boundary format in V0• • •Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) × • • • × SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 • • •Vp such that Stab(A)0 _ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) × • • • × SL(Vp)-orbit containing the identity matrices, according to [1]. 


Prolongements en fonctions algébriquement constructibles  

Palabras Clave: semialgebraic sets, algebraically constructible functions, quadratic forms.
In this paper we consider the following question: Let S be a semialgebraic subset of a real algebraic set V , and let ' : S ! Z be a function on S. Is ' the restriction of an algebraically constructible function on V , i.e. a sum of signs of polynomials on V ? We give an effective method to answer this question when '(S) _ {−1, 1} or dimS _ 2 or S is basic. 


The Range of a Contractive Projection in Lp(H)  

Palabras Clave: Contractive projections, Vector-valued Lp-spaces.
We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a p-direct sum of Hilbertvalued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < 1 the class Cp of p-direct sums of Hilbertvalued Lp-spaces is axiomatizable (in the class of all Banach spaces).

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