Artículos (Análisis Matemático)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10809

Examinar

Mostrando 1 - 20 de 781

The ball fixed point property in spaces of continuous functions
(Springer, 2025-06-22) Avilés, Antonio; Japón Pineda, María de los Ángeles; Lennard, Christopher J.; Martínez Cervantes, Gonzalo; Stawski, Adam; Análisis Matemático; FQM127: Análisis Funcional no Lineal
A Banach space X has the ball fixed point property (BFPP) if for every closed ball B and for every nonexpansive mapping T:B→B, there is a fixed point. We study the BFPP for C(K)-spaces. Our goal is to determine topological properties over K that may determine the failure or fulfillment of the BFPP for the space of continuous functions C(K). We prove that the class of compact spaces K for which the BFPP holds lies between the class of extremally disconnected compact spaces and the class of compact F-spaces. We give a family of examples of F-spaces K for which the BFPP fails. As a result, we prove that for every cardinal κ, κ-order completeness or κ-hyperconvexity of C(K) are not enough for the BFPP and we obtain that ℓ∞/c0=C(N∗) fails BFPP under the Continuum Hypothesis. The space C([0,+∞)∗) is also analyzed. It is left as an open problem whether all compact spaces for which the BFPP holds are in fact the extremally disconnected compact sets.
Short proofs of Cambern's 1968 theorem and its generalizations applicable to fixed point theory
(Akademicka Platforma Czasopism, 2026-03-01) Japón Pineda, María de los Ángeles; Malec, Marek; Piasecki, Lukasz; Análisis Matemático; FQM127: Análisis Funcional no Lineal
First we provide short, elementary and self-contained proofs of all known results concerning the lower bounds of the Banach–Mazur distances between the space 𝑐0 of sequences converging to 0 and other ℓ1-preduals isomorphic to 𝑐0. Then, we use our technique to obtain lower bounds for the Banach–Mazur distances between any two ℓ1-preduals 𝑋 and 𝑌. Our estimate depends only on the smallest radiuses 𝑟∗⁡(𝑋) and 𝑟∗⁡(𝑌) of the closed balls in ℓ1 containing, respectively, all 𝜎⁡(ℓ1,𝑋)-cluster points and all 𝜎⁡(ℓ1,𝑌)-cluster points of the set of all extreme points of the closed unit ball in ℓ1, and for any values of 𝑟∗⁡(𝑋) and 𝑟∗⁡(𝑌) it is sharp. We apply this result to show that for every ℓ1-predual 𝑋 with 𝑟∗⁡(𝑋) <1, every ℓ1-predual 𝑌 with the distance from 𝑋 strictly less than 3−𝑟∗⁡(𝑋) 1+𝑟∗⁡(𝑋) induces a weak∗ topology on ℓ1 such that ℓ1 has the 𝜎⁡(ℓ1,𝑌)-fixed point property for nonexpansive mappings. If we additionally assume that the standard basis in ℓ1 is 𝜎⁡(ℓ1,𝑋)-convergent, then the estimate is precise. The same holds if the standard basis in ℓ1 has a finite number of 𝜎⁡(ℓ1,𝑋)-cluster points and each of them has a finite number of non-zero coordinates. It should be emphasized that the value of this constant was known only for the space 𝑐0 so far.
The Bergman and the growth numbers of domains and hyperbolic geometry
(Elsevier, 2027-01) Contreras Márquez, Manuel Domingo; Cruz Zamorano, Francisco José; Rodríguez Piazza, Luis; Matemática Aplicada II; Análisis Matemático; Ministerio de Ciencia e Innovación (MICIN). España; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; Agencia Estatal de Investigación. España
In this article we completely characterize the Bergman number of general domains. Namely, we prove that the Bergman number of a hyperbolic unbounded domain can be calculated in terms of the asymptotic behavior of its hyperbolic metric near infinity. To obtain the proof of this result we first work in the setting of growth spaces, defining the growth number of a domain. Later, we prove an equality relating the Bergman number and the growth number of domains. We also provide examples of domains with prescribed Bergman number which have zero Hardy number, solving a question posed previously by Betsakos and Cruz-Zamorano. At the end, a similar idea is treated for the case of Bloch-type spaces.
Zeros of Linear Combinations of Orthogonal Polynomials
(Springer, 2026-06-18) Durán Guardeño, Antonio José; Análisis Matemático; FQM262: Teoría de la Aproximación
Given a sequence of orthogonal polynomials (pn)n with respect to a positive measure in the real line, we study the real zeros of finite combinations of K+1 consecutive orthogonal polynomials of the form qn(x)=K∑j=o yjPn-j(x), n≥K, where yj,J=0,...,K, are real numbers with y0=1,yK=0 (which do not depend on n). We prove that for every positive measure µ there always exists a sequence of orthogonal polynomials with respect to µ such that all the zeros of the polynomial qn above are real and simple for n≥n0, where n0 is a positive integer depending on K and the yj’s.
Traveling motility of actin lamellar fragments under spontaneous symmetry breaking
(Elsevier, 2025-09-26) García, Claudia; Magliocca, Martina; Meunier, Nicolas; Análisis Matemático
Cell motility is connected to the spontaneous symmetry breaking of a circular shape. In, Blanch-Mercader and Casademunt performed a nonlinear analysis of the minimal model proposed by Callan and Jones and numerically conjectured the existence of traveling solutions once that symmetry is broken. In this work, we prove analytically that conjecture by means of nonlinear bifurcation techniques.
Stochastic and incremental subgradient methods for convex optimization on Hadamard spaces
(Springer, 2026-03-11) Goodwin, Ariel; Lewis, Adrián S.; López Acedo, Genaro; Nicolae, Adriana; Análisis Matemático; FQM127: Análisis Funcional no Lineal
As a foundation for optimization, convexity is useful beyond the classical settings of Euclidean and Hilbert space. The broader arena of nonpositively curved metric spaces, which includes manifolds like hyperbolic space, as well as metric trees and more general CAT(0) cubical complexes, supports primal tools like proximal operations for geodesically convex functions. However, the lack of linear structure in such spaces complicates dual constructions like subgradients. To address this hurdle, we introduce a new type of subgradient for functions on Hadamard spaces, based on Busemann functions. Our notion supports generalizations of classical stochastic and incremental subgradient methods, with guaranteed complexity bounds. We illustrate with subgradient algorithms for p-mean problems in general Hadamard spaces, in particular computing medians in BHV tree space.
Radon transforms with small derivatives anddistance inequalities for convex bodies
(arXiv, 2023-12-28) Haddad, Julián Eduardo; Koldobsky, Alexander; Análisis Matemático
Generalizing the slicing inequality for functions on convex bodies from [11], it was proved in [4] that there exists an absolute constant c so that for any (Formula Presented) which is not an odd integer, any origin-symmetric convex body K of volume one in (Formula Presented) and any infinitely smooth probability density/on K we have (Formula Presented) is the Radon transform of f, and the fractional derivative of the order q is taken with respect to the variable (Formula Presented). In this note we show that there exist an origin-symmetric convex body K of volume 1 in Rn and a continuous probability density g on K so that (Formula Presented) this was proved in [5, 6], and it was used there to obtain a lower estimate for the maximal outer volume ratio distance from an arbitrary origin-symmetric convex body K to the class of intersection bodies. We extend the latter result to the class (Formula Presented) of bodies in (Formula Presented) that embed in (Formula Presented). Namely, for every (Formula Presented) there exists an origin-symmetric convex body K in (Formula Presented).
Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution
(Springer, 2026-01-23) Dall’Aglio, Andrea; Magliocca, Martina; Segura de León, Sergio; Análisis Matemático
In this paper, we study existence and regularity for solutions to parabolic equations having a superlinear lower order term depending on both the solution and its gradient. Two different situations are analyzed. On the one hand, we assume that the initial datum belongs to an Orlicz space of exponentially summable functions. On the other, data in an appropriate Lebesgue space satisfying a smallness condition are considered. Our results are coherent with those of previous papers in similar frameworks.
On the volume of convolution bodies in the plane
(Springer, 2025-08-18) Haddad, Julián Eduardo; Análisis Matemático
For every convex body K ⊂ Rn and ∫ E (0,1), the ∫-convolution body of K is the set of x E Rn for which |K Ω (K + x)|n ≥∫|K|n. We show that for n=2 and any ∫ E (0,1), ellipsoids do not maximize the volume of the ∫-convolution body of K, when K runs over all convex bodies of a fixed volume. This behavior is somehow unexpected and contradicts the limit case ∫ → 1, which is governed by the Petty projection inequality.
New Functional Inequalities with Applications to the Arctan-Fast Diffusion Equation
(Springer, 2025-04-15) Granero Belinchón, Rafael; Magliocca, Martina; Ortega, Alejandro; Análisis Matemático
In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads Then, these inequalities are used in the study of the nonlinear arctan-fast diffusion equation For this highly nonlinear PDE, we establish a number of well-posedness results and qualitative properties.
Historia y enseñanza de las matemáticas: La chistera del capitán Cook
(Universidad de Almería, 2026-01-30) Durán Guardeño, Antonio José; Análisis Matemático; FQM262: Teoría de la Aproximación
Global-in-Time Estimates for the 2D One-Phase Muskat Problem with Contact Points
(Springer, 2026-05-02) Bocchi, Edoardo; Castro, Angel; Gancedo García, Francisco; Análisis Matemático; FQM104: Análisis Matemático
In this paper, we study the dynamics of a two-dimensional viscous fluid evolving through a porous medium or a Hele-Shaw cell, driven by gravity and surface tension. A key feature of this study is that the fluid is confined within a vessel with vertical walls and below a dry region. Consequently, the dynamics of the contact points between the vessel, the fluid and the dry region are inherently coupled with the surface evolution. A similar contact scenario was recently analyzed for more regular viscous flows, modeled by the Stokes (Guo and Tice, Arch Ration Mech Anal 227(2):767–854, 2018) and Navier–Stokes (Guo and Tice, J Eur Math Soc 26(4):1445–1557, 2024) equations. Here, we adopt the same framework but use the more singular Darcy’s law for modeling the flow. We prove global-in-time a priori estimates for solutions initially close to equilibrium. Taking advantage of the Neumann problem solved by the velocity potential, the analysis is carried out in non-weighted L2-based Sobolev spaces and without imposing restrictions on the contact angles.
Effects of fast diffusion in the logistic equation with refuge
(Elsevier, 2025-03-19) Ramos, Vinicius Kobayashi; Santos, Carlos Alberto; Suárez Fernández, Antonio; Análisis Matemático; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
This paper studies the behaviour of the positive solution of a logistic equation with respect to a space dependent diffusion rate. The equation also includes a refuge, a zone where the species grows freely. In contrast to the case of homogeneous diffusion coefficient, where the species dies for large diffusion regardless of the birth rate, we show that the species may die, persist or growth indefinitely, depending on the size of the birth rate, for a large increasing of this diffusion rate in a certain region of the space, even more, this growth causes blow up in this region as well as in the refuge.
Influence of the Reynolds number on non-Newtonian flow in thin porous media
(Taylor & Francis, 2026-07-08) Anguiano Moreno, María; Bonnivard, Matthieu; Suárez Grau, Francisco Javier; Análisis Matemático; Ecuaciones Diferenciales y Análisis Numérico; Agence Nationale de la Recherche. France; FQM104: Análisis Matemático
We study the effect of the Reynolds number on the flow of a generalized Newtonian fluid through a thin porous medium in R^3. This medium is a domain of thickness ε ≪ 1, which is perforated by periodically distributed solid cylinders of size ε. We consider the nonlinear stationary Navier–Stokes system with viscosity following the Carreau law with flow index r, with 1 < r < +∞. The Reynolds number is assumed to scale as ε^{−γ} , where γ is a real constant. The methodology combines homogenization theory with dimension reduction techniques appropriate for thin domains. We perform a scaling in the vertical direction and introduce an appropriate extension operator to handle the perforated geometry. The treatment of the inertial terms, which represents a major analytical challenge, relies on a combination of refined interpolation techniques and sharp estimates for the extended pressure fields. Our main theoretical result identifies the existence of a critical Reynolds number of order 1/ε (i.e., γ = 1), independent of the flow index r, that separates regimes where inertial terms vanish or persist in the homogenized limit. Specifically, for Reynolds number of order smaller than or equal to 1/ε, the inertial term becomes negligible in the homogenized limit (giving linear Darcy’s law for γ < 1 and nonlinear Darcy’s law for γ = 1), whereas for Reynolds numbers greater than the critical value (γ > 1), inertial effects are expected, and the classical Darcy’s law approximation fails. Finally, we propose a new numerical method for solving the nonlinear Darcy’s law describing the effective flow in the critical case. We present a mesh convergence analysis for the 3D cell describing the periodic structure of the material, and study the influence of rheological and geometrical parameters of the flow on the resulting numerical solutions.
Homogenization of a Stokes problem with non homogeneous Fourier boundary conditions in a thin perforated domain
(World Scientific, 2026-06-26) Anguiano Moreno, María; Suárez Grau, Francisco Javier; Análisis Matemático; Ecuaciones Diferenciales y Análisis Numérico; FQM104: Análisis Matemático
We consider a viscous fluid obeying the 3D Stokes system in a thin layer Ωε ⊂ R3 of thickness 0 < hε ≪ 1, which is perforated by ε-periodically distributed cylinder shaped obstacles of size 0 < ε ≪ 1. On the boundary of the obstacles, we prescribe non homogeneous Fourier boundary conditions with a parameter αε ∈ (0, +∞). Depending on the relation between ε and hε, we prove the convergence of the homogenization process when ε goes to zero for different values of αε. As a result, we derive different 2D Darcy’s laws taking into account the microstructure of the domain by means of local problems. The dimensions of the local problems are 2D or 3D depending on the relation between ε and hε, i.e. if hε ≫ ε or hε ≈ ε, respectively. Moreover, depending on the relation between αε and ε^{−1}, the boundary conditions of the local problems on the reference obstacle are of three types: homogeneous Dirichlet if αε ≫ ε^{−1}, non homogeneous Fourier if αε ≈ ε^{−1}, or homogeneous Fourier boundary conditions if αε ≪ ε^{−1}.
Complex symmetric Toeplitz operators through representation theory tools
(Springer, 2026-06-22) Heredia Muñoz, Esteban; Sánchez Nungaray. Armando; Jiménez Gómez, Carlos Hugo; Análisis Matemático
Proceeding through a representation theoretic approach, we study the family of Toeplitz operators on the weighted Bergman space H²α (Bn) whose symbols are invariant under the action of the semidirect group S∆ X Tn, where S∆ is a subgroup of permutations. Associating a suitable partition ∆ we associated the conjugation JA on the Bergman space. Moreover we characterize the complex symmetric Toeplitz operators Tα and Tα(r)tpt-q with respect the conjugation JA, where the symbols are invariant under the action of S∆ X Tn.
Frequently Hypercyclic Sequences of Differential Operators on the Space of Entire Functions
(Springer, 2026-06-01) Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio; Análisis Matemático; FQM127: Análisis Funcional no Lineal
A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on an appropriate closed annulus, in the boundary of which the modulus of each term of the sequence is in some sense controlled by the preceding ones or the following ones.
New results in analysis of Orlicz-Lorentz spaces
(Elsevier, 2026-01-13) Bernal González, Luis; Rodríguez Vidanes, Daniel L.; Seoane Sepúlveda, Juan Benigno; Tag, Hyung Joon; Análisis Matemático; FQM127: Análisis Funcional no Lineal
In this article, we investigate the existence of closed vector subspaces (i.e. spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces Λyw equipped with the Luxemburg norm. If a family of Orlicz functions (yn)∞ n=1 satisfies certain order relations with respect to a given Orlicz function φ, the subset of the order-continuous subspace (Λyw)α whose elements do not belong to U∞n=1 Λyn,w is spaceable, and even maximal-spaceable when φ satisfies the ∆2-condition. We also show that this subset is either residual or empty. In addition, sufficient conditions for this subset not being (α, β)-spaceable are provided. A similar analysis is also performed on the subset Λy,w / (Λy,w)α when φ does not satisfy the ∆2-condition. The comparison between different Orlicz-Lorentz spaces is characterized via the generating pairs (y,w). For a fixed Orlicz function that satisfies the ∆2∞-condition, we provide a characterization of disjointly strictly singular inclusion operators between Orlicz-Lorentz spaces with different weights. As a consequence, there are certain subsets of Orlicz-Lorentz spaces on [0,1] for which the lineability problem is not valid. Moreover, various types of (α, β)-lineability and pointwise lineability properties on other nonlinear subsets of Orlicz-Lorentz spaces are examined. These results extend a number of previously known results in Orlicz and Lorentz spaces.
The Bloch–Nevanlinna problem under lineability
(Springer, 2023-03-28) Bernal González, Luis; Bonilla, A.; Análisis Matemático; FQM127: Análisis Funcional no Lineal
The original version of the celebrated Bloch–Nevanlinna problem asked whether there exists or not a holomorphic function in the unit disc of bounded characteristic whose derivative is not of bounded characteristic. This problem has been solved in the affirmative by a number of mathematicians. Starting from a result on topological genericity of this class of functions due to Hahn, our work intends—under an algebraic as well as a topological point of view—to contribute to this topic. Specifically, the family of solutions of the Bloch–Nevanlinna problem is proved to be residual in appropriate topological spaces, and it contains, except for the zero function, dense maximal dimensional vector subspaces, large linear algebras and infinite-dimensional Banach spaces.
Dichotomy between operators acting of finite and infinite dimensional Hilbert spaces
(arXiv, 2022-03-01) Bernal González, Luis; Moslehian, M.S.; Seoane Sepúlveda, Juan Benigno; Análisis Matemático; FQM127: Análisis Funcional no Lineal
In this expository article, we give several examples showing how drastically different can be the behavior of operators acting on finite versus infinite dimensional Hilbert spaces. This essay is written as in such a friendly-reader to show that the situation in the infinite dimensional setting is trickier than the finite one.

Examinar

Envíos recientes