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Autor Azagra Rueda, Daniel |
Documentos disponibles escritos por este autor (46)
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Let H be a Hilbert space, E?H be an arbitrary subset and f:E?R, G:E?H be two functions. We give a necessary and sufficient condition on the pair (f,G) for the existence of a convex function F?C1,1(H) such that F=f and ?F=G on E. We also show tha[...]![]()
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We prove a general form of a fixed point theorem for mappings from a Riemannian manifold into itself which are obtained as perturbations of a given mapping by means of general operations which in particular include the cases of sum (when a Lie g[...]![]()
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Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2003-07-01We establish approximate Rolle's theorems for the proximal subgradient and for the generalized gradient. We also show that an exact Rolle's theorem for the generalized gradient is completely false in all infinite-dimensional Banach spaces (even [...]![]()
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We characterize the class of separable Banach spaces X such that for every continuous function f : X -> Rand for every continuous function epsilon : X -> (0, +infinity) there exists a C-1 smooth function g: X -> R for which vertical bar f(x) [...]![]()
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Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f : X -> R be bounded and Lipschitz, with uniformly continuous derivative. Then, for each epsilon > 0, there exists a[...]![]()
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Azagra Rueda, Daniel ; Gómez Gil, Javier ; Fry, Robb ; Lovo, Mauricio ; Jaramillo Aguado, Jesús Ángel | Oxford University Press | 2005-03We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ? : X ? (0, ?), there exists a Cp-smoo[...]![]()
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In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible invarian[...]![]()
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We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessaril[...]![]()
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The authors show that for every closed convex set C in a separable Banach space there is a nonnegative C1 convex function f such that C = {x: f(x) = 0}. The key is to show this for a closed halfspace. This result has several attractive consequen[...]![]()
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Azagra Rueda, Daniel ; Fabián, M. ; Jiménez Sevilla, María del Mar | University of Toronto Press | 2005We establish sufficient conditions on the shape of a set A included in the space Ln s (X; Y ) of the n-linear symmetric mappings between Banach spaces X and Y , to ensure the existence of a Cn-smooth mapping f : X ¡! Y , with bounded support, an[...]![]()
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In this paper we establish several results which allow to find fixed points and zeros of set-valued mappings on Riemannian manifolds. In order to prove these results we make use of subdifferential calculus. We also give some useful applications.![]()
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We consider the generalized evolution of compact level sets by functions of their normal vectors and second fundamental forms on a Riemannian manifold M. The level sets of a function u;M -> R evolve in such a way whenever u solves an equation u[...]![]()
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Azagra Rueda, Daniel ; Jiménez Sevilla, María del Mar | Universidad de Extremadura, Departamento de Matemáticas | 2002While the topological and geometrical properties of convex bodies in Banach spaces are quite well understood (including their topological and smooth classification), much less is known about the structure of starlike bodies. Starlike bodies are [...]![]()
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Let U subset of R-d be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f:U -> R can be approximated by real analytic convex functions, uniformly on all of U. We also show that C-0-fine approximation[...]![]()
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We show that if X is a Banach space whose dual X* has an equivalent locally uniformly rotund (LUR) norm, then for every open convex U subset of X, for every real number epsilon > 0, and for every continuous and convex function f : U -> R (not [...]![]()
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Heterochrony, evolutionary modifications in the rates and/or the timing of development, is widely recognized as an important agent of evolutionary change. In this paper, we are concerned with the detection of this evolutionary mechanism through [...]![]()
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We show how an operation of inf-convolution can be used to approximate convex functions with $C^1$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other pr[...]![]()
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Starlike bodies are interesting in nonlinear functional analysis because they are strongly related to bump function sand to n-homogeneous polynomials on Banach spaces, and their geometrical proper ties are thus worth studying. In this paper we d[...]![]()
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Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2006-11-01We establish a maximum principle for viscosity subsolutions and supersolutions of equations of the form u(t) + F(t, d(x)u) = 0, u(0, x) = u(0)(x), where u(0): M -> R is a bounded uniformly continuous function, M is a Riemannian manifold, and F:[...]![]()
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Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando | Elsevier | 2005-03-15We establish some perturbed minimization principles, and we develop a theory of subdifferential calculus, for functions defined on Riemannian manifolds. Then we apply these results to show existence and uniqueness of viscosity solutions to Hamil[...]![]()
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We prove that every function f:Rn?R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n?1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof,[...]![]()
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The paper deals with the question, what can be said about smooth negligibility of compacta in those Banach spaces with smooth partitions of unity? It is inspired by the following theorem of Victor Klee and related results: If X is a non-reflexiv[...]