Análisis Matemático

URI permanente para esta comunidadhttps://hdl.handle.net/11441/10808

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2º Congreso de Jóvenes Investigadores
(Real Sociedad Matematica Española, 2013) Gancedo García, Francisco; Muro Jiménez, Fernando; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM104: Análisis Matemático; Universidad de Sevilla. FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
A Birkhoff theorem for Riemann surfaces
(Rocky Mountain Mathematics Consortium, 1998) Montes Rodríguez, Alfonso; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Investigación Científica y Técnica (DGICYT). España
A classical theorem of Birkhoff asserts that there exists an entire function f such that the sequence of function {/(z + n)}n≥o is dense in the space of entire functions. In this paper we give sufficient conditions on a Riemann surface R and on a given sequence {φn}n≥o of holomorphic self-mappings of R such that there exists a holomorphic function f on R such that {f o φn}n≥0 is dense in the space of holomorphic functions on R. The necessity of these conditions is examined. In particular, we characterize the Riemann surfaces R and the sequences {φn}n≥0 of automorphisms of R. for which there exists a holomorphic function f on R with the property that the sequence {f o φn] n≥o is dense in the space of the holomorphic functions on R.
A Bp condition for the strong maximal function
(American Mathematical Society, 2014-11) Liu, Liguang; Luque Martínez, Teresa; Universidad de Sevilla. Departamento de Análisis Matemático; National Natural Science Foundation of China; Ministerio de Ciencia e Innovación (MICIN). España
A strong version of the Orlicz maximal operator is introduced and a natural Bp condition for the rectangle case is defined to characterize its boundedness. This fact let us to describe a sufficient condition for the two weight inequalities of the strong maximal function in terms of power and logarithmic bumps. Results for the multilinear version of this operator and for others multi(sub)linear maximal functions associated with bases of open sets are also studied.
A characterization of 3D steady Euler flows using commuting zero-flux homologies
(Cambridge, 2020-02-10) Peralta Salas, Daniel; Rechtman, Ana; Torres de Lizaur, Francisco Javier; Universidad de Sevilla. Departamento de Análisis matemático; Universidad de Sevilla. FQM104: Analisis Matematico
We characterize, using commuting zero-flux homologies, those volumepreserving vector fields on a 3-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan’s homological characterization of geodesible flows in the volume-preserving case. As an application, we show that steady Euler flows cannot be constructed using plugs (as in Wilson’s or Kuperberg’s constructions). Analogous results in higher dimensions are also proved.
A characterization of the classical orthogonal discrete and q-polynomials
(Elsevier, 2007-04-01) Alfaro García, Manuel; Álvarez Nodarse, Renato; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoría de la Aproximación
In this paper we present a new characterization for the classical discrete and q-classical (discrete) polynomials (in the Hahn's sense).
A characterization of weak proximal normal structure and best proximity pairs
(Springer, 2022-02-11) Digar, Abhik; Espínola García, Rafael; Kosuru, G. Sankara Raju; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
The aim of this paper is to address an open problem given in [Kirk et al. in J Math Anal Appl 463:461–476, (2018)]. We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove the existence of a best proximity pair in the setting of reflexive Banach spaces.
A continuation method for weakly contractive mappings under the interior condition
(Hindawi, 2009) Ariza Ruiz, David; Jiménez Melado, Antonio; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
Recently, Frigon proved that, for weakly contractive maps, the property of having a fixed point is invariant by a certain class of homotopies, obtaining as a consequence a Leray-Schauder alternative for this class of maps in a Banach space. We prove here that the Leray-Schauder condition in the aforementioned result can be replaced by a modification of it, the interior condition. We also show that our arguments work for a certain class of generalized contractions, thus complementing a result of Agarwal and O’Regan.
A continuation method for weakly Kannan maps
(SpringerOpen, 2010) Ariza Ruiz, David; Jiménez Melado, Antonio; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Educación y Ciencia (MEC). España; Junta de Andalucía; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
The first continuation method for contractive maps in the setting of a metric space was given by Granas. Later, Frigon extended Granas theorem to the class of weakly contractive maps, and recently Agarwal and O’Regan have given the corresponding result for a certain type of quasicontractions which includes maps of Kannan type. In this note we introduce the concept of weakly Kannan maps and give a fixed point theorem, and then a continuation method, for this class of maps.
A criterion of weak compactness for operators on subspaces of Orlicz spaces
(Hindawi, 2008) Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez Piazza, Luis; Universidad de Sevilla. Departamento de Análisis Matemático
We give a criterion of weak compactness for the operators on the Morse-Transue space MΨ , the subspace of the Orlicz space LΨ generated by L∞.
A dynamical characterization of sub-Arakelian subsets
(Elsevier, 2013-09-15) Calderón Moreno, María del Carmen; Prado Bassas, José Antonio; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
We are going to characterize those sets which can be covered by an Arakelian set in terms of dynamical properties of entire functions via similarities. Moreover, if we consider the set of universal entire functions via similarities that are bounded on such a sub-Arakelian set, then it is shown that its algebraic size is as large as possible. As a consequence, we prove that the set of universal entire functions bounded on every (straight) line is algebraically large.
A family of quasi-birth-and-death processes coming from the theory of orthogonal matrix polynomials
(2008) Domínguez de la Iglesia, Manuel; Grünbaum, Francisco Alberto; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM262: Teoría de la Aproximación
A fixed point theorem for weakly Zamfirescu mappings
(Elsevier, 2011-03-01) Ariza Ruiz, David; Jiménez Melado, Antonio; López Acedo, Genaro; Universidad de Sevilla. Departamento de Análisis Matemático; Junta de Andalucía; Dirección General de Enseñanza Superior. España; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
In [13] T. Zamfirescu, Fixed point theorems in metric spaces, Arch. Math. 23 (1972), 292–298. Zamfirescu gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu’s fixed point theorem to the class of weakly Zamfirescu maps. A continuation method for this class of maps is also given.
A Fredholm mapping of index zero
(Korean Mathematical Society, 2008) Soriano Arbizu, José María; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Enseñanza Superior. España; Junta de Andalucía
Sufficient conditions are given to assert that between any two Banach spaces over K Fredholm mappings share exactly N values in a specific open ball. The proof of the result is constructive and is based upon continuation methods.
A generalization of the classical Laguerre polynomials
(Springer, 1995) Álvarez Nodarse, Renato; Marcellán Español, Francisco; Universidad de Sevilla. Departamento de Análisis Matemático; Instituto de Cooperación Iberoamericana (ICI); Comisión Interministerial de Ciencia y Tecnología (CICYT). España
We consider a modi cation of the gamma distribution by adding a discrete measure supported in the point x = 0. For large n we analyze the existence of orthogonal polynomials with respect to such a distribution. Finally we represent them as the hypergeometric function 3F3:
A geometrical coefficient implying the fixed point property and stability results
(University of Houston, 1996) Domínguez Benavides, Tomás; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Investigación Científica y Técnica (DGICYT). España; Junta de Andalucía
In this paper we define a new geometric constant M(X) in Banach spaces such that X has the fixed point property for nonexpansive mappings if M(X) > 1. We prove that M(X) •_ WCS(X), the inequality being strict in many important classes of Banach spaces and we obtain lower bounds for M(X) based upon either the modulus of near uniform smoothness or the modulus of the Opia] property of the conjugated space. We show that this new constant gives us stability results for the fixed point property with respect to œp-spaces which improve all previous results.
À la carte recurrence relations for continuous and discrete hypergeometric functions
(Sociedad Española de Matemática Aplicada, 2011-09) Álvarez Nodarse, Renato; Universidad de Sevilla. Departamento de Análisis Matemático; Dirección General de Enseñanza Superior. España; Junta de Andalucía
We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometric-type functions not only for the continuous case but also for the discrete and q-linear cases, respectively. Some applications in Quantum Physics are discussed.
A local spectral condition for strong compactness with some applications to bilateral weighted shifts
(American Mathematical Society, 2014-01) Lacruz Martín, Miguel Benito; Romero de la Rosa, María del Pilar; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Ciencia e Innovación (MICIN). España; Junta de Andalucía
An algebra of bounded linear operators on a Banach space is said to be strongly compact if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be strongly compact if the algebra with identity generated by the operator is strongly compact. Our interest in this notion stems from the work of Lomonosov on the existence of invariant subspaces. We provide a local spectral condition that is sufficient for a bounded linear operator on a Banach space to be strongly compact. This condition is then applied to describe a large class of strongly compact, injective bilateral weighted shifts on Hilbert spaces, extending earlier work of Fernández-Valles and the first author. Further applications are also derived, for instance, a strongly compact, invertible bilateral weighted shift is constructed in such a way that its inverse fails to be a strongly compact operator.
A lot of “counterexamples” to Liouville's theorem
(Elsevier, 1996-08-01) Bernal González, Luis; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j. Moreover, it is shown the existence of an entire function with infinite growth index satisfying the latter property.
A lower bound for the equilateral number of normed spaces
(American Mathematical Society, 2008) Swanepoel, Konrad J.; Villa Caro, Rafael; Universidad de Sevilla. Departamento de Análisis Matemático; South African National Research Foundation; Dirección General de Enseñanza Superior. España
We show that if the Banach-Mazur distance between an n-dimensional normed space X and ℓ n∞ is at most 3/2, then there exist n + 1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an arbitrary n-dimensional normed space admits at least e c √ log n equidistant points, where c > 0 is an absolute constant. We also show that there exist n equidistant points in spaces sufficiently close to ℓ n p , 1 < p < ∞.
A maximum principle for the Muskat problem for fluids with different densities
(Springer, 2009-03) Córdoba Gazolaz, Diego; Gancedo García, Francisco; Universidad de Sevilla. Departamento de Análisis Matemático; Ministerio de Educación y Ciencia (MEC). España; Junta de Castilla-La Mancha; Universidad de Sevilla. FQM104: Analisis Matematico
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for the L∞ norm of the free boundary.

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