Scielo RSS <![CDATA[Revista de la Unión Matemática Argentina]]> http://www.scielo.org.ar/rss.php?pid=0041-693220080002&lang=en vol. 49 num. 2 lang. en <![CDATA[SciELO Logo]]> http://www.scielo.org.ar/img/en/fbpelogp.gif http://www.scielo.org.ar <![CDATA[On the life and work of Mischa Cotlar]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200001&lng=en&nrm=iso&tlng=en <![CDATA[Matrix spherical functions and orthogonal polynomials: An instructive example]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200002&lng=en&nrm=iso&tlng=en In the scalar case, it is well known that the zonal spherical functions of any compact Riemannian symmetric space of rank one can be expressed in terms of the Jacobi polynomials. The main purpose of this paper is to revisit the matrix valued spherical functions associated to the complex projective plane to exhibit the interplay among these functions, the matrix hypergeometric functions and the matrix orthogonal polynomials. We also obtain very explicit expressions for the entries of the spherical functions in the case of 2 x 2 matrices and exhibit a natural sequence of matrix orthogonal polynomials, beyond the group parameters. <![CDATA[Minimal hermitian matrices with fixed entries outside the diagonal]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200003&lng=en&nrm=iso&tlng=en We survey some results concerning the problem of finding the complex hermitian matrix or matrices of least supremum norm with variable diagonal. Some cualitative general results are given and more specific descriptions are shown for the 3 × 3 case. We also comment some results and examples concerning this approximation problem. <![CDATA[Weighted inequalities for generalized fractional operators]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200004&lng=en&nrm=iso&tlng=en In this note we present weighted Coifman type estimates, and two-weight estimates of strong and weak type for general fractional operators. We give applications to fractional operators given by an homogeneous function, and by a Fourier multiplier. The complete proofs of these results appear in the work [5] done jointly with Ana L. Bernardis and María Lorente. <![CDATA[Restriction of the Fourier transform]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200005&lng=en&nrm=iso&tlng=en This paper contains a brief survey about the state of progress on the restriction of the Fourier transform and its connection with other conjectures. It contains also a description of recent related results that we have obtained. <![CDATA[Quaternions and octonions in Mechanics]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200006&lng=en&nrm=iso&tlng=en This paper contains a brief survey about the state of progress on the restriction of the Fourier transform and its connection with other conjectures. It contains also a description of recent related results that we have obtained. <![CDATA[A Model for the Thermoelastic Behavior of a Joint-Leg-Beam System for Space Applications]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200007&lng=en&nrm=iso&tlng=en Rigidizable-Inflatable (RI) materials offer the possibility of deployable large space structures (C.H.M. Jenkins (ed.), Gossamer Spacecraft: Membrane and Inflatable Structures Technology for Space Applications, Progress in Aeronautics and Astronautics, 191, AIAA Pubs., 2001) and so are of interest in applications where large optical or RF apertures are needed. In particular, in recent years there has been renewed interest in inflatable-rigidizable truss-structures because of the efficiency they offer in packaging during boost-to-orbit. However, much research is still needed to better understand dynamic response characteristics, including inherent damping, of truss structures fabricated with these advanced material systems. One of the most important characteristics of such space systems is their response to changing thermal loads, as they move in and out of the Earth's shadow. We study a model for the thermoelastic behavior of a basic truss componentconsisting of two RI beams connected through a joint subject to solar heating. Axial and transverse motions as well as thermal response of the beams with thermoelastic damping are taking into account. The model results in a couple PDE-ODE system. Well-posedness and stability results are shown and analyzed. <![CDATA[Admissible restriction of holomorphic discrete series for exceptional groups]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200008&lng=en&nrm=iso&tlng=en In this note, we give results about the restriction of a holomorphic discrete series of an exceptional simple Lie real group to a subgroup. <![CDATA[Best Local Approximations by Abstract Norms with Non-homogeneous Dilations]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200009&lng=en&nrm=iso&tlng=en We introduce a concept of best local approximation using abstract norms and non-homogeneous dilations. The asymptotic behavior of the normalized error function as well as the limit of some net of best approximation polynomials <IMG SRC="/img/revistas/ruma/v49n2/2a090x.png">as <IMG SRC="/img/revistas/ruma/v49n2/2a091x.png">are studied. <![CDATA[Hypergeometric functions and binomials]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200010&lng=en&nrm=iso&tlng=en We highlight the role of primary decomposition of binomial ideals in a commutative polynomial ring, in the description of the holonomicity, the holonomic rank, and the shape of solutions of multivariate hypergeometric differential systems of partial differential equations. <![CDATA[The problem of entanglement of quantum states]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200011&lng=en&nrm=iso&tlng=en We give a brief and incomplete survey of the problem of entanglement of states of composite quantum systems. <![CDATA[A survey on hyper-Kähler with torsion geometry]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200012&lng=en&nrm=iso&tlng=en Manifolds with special geometric structures play a prominent role in some branches of theoretical physics, such as string theory and supergravity. For instance, it is well known that supersymmetry requires target spaces to have certain special geometric properties. In many cases these requirements can be interpreted as restrictions on the holonomy group of the target space Riemannian metric. However, in some cases, they cannot be expressed in terms of the Riemannian holonomy group alone and give rise to new geometries previously unknown to mathematicians. An example of this situation is provided by hyper-Kähler with torsion (or HKT) metrics, a particular class of metrics which possess a compatible connection with torsion whose holonomy lies in Sp(n). A survey on recent results on HKT geometry is presented. <![CDATA[The Hilbert transform and scattering]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200013&lng=en&nrm=iso&tlng=en Through the prism of abstract scattering, and the invariant forms acting in them, we discuss the Hilbert transform in weighted Lp spaces in one and several dimensions. <![CDATA[Erratum to "Some aspects of the history of applied mathematics in Argentina"]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200014&lng=en&nrm=iso&tlng=en Through the prism of abstract scattering, and the invariant forms acting in them, we discuss the Hilbert transform in weighted Lp spaces in one and several dimensions. <![CDATA[2007/ LVII Reunión anual de Comunicaciones Científicas de la Unión Matemática Argentina y XXX Reunión de Educación Matemática]]> http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0041-69322008000200015&lng=en&nrm=iso&tlng=en Through the prism of abstract scattering, and the invariant forms acting in them, we discuss the Hilbert transform in weighted Lp spaces in one and several dimensions.