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Autor Azagra Rueda, Daniel |
Documentos disponibles escritos por este autor (46)
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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[...]![]()
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Azagra Rueda, Daniel ; Jiménez Sevilla, María del Mar ; Deville, Robert | Cambridge University Press | 2003-01We study the size of the range of the derivatives of a smooth function between Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure the existence of a C-p smooth (Frechet smooth or a continuous G (a) over cap teaux[...]![]()
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We study the size of the sets of gradients of bump functions on the Hilbert space l(2), and the related question as to how small the set of tangent hyperplanes to a smooth bounded starlike body in l(2) can be. We find that those sets can be quit[...]![]()
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Starlike bodies are interesting in nonlinear analysis because they are strongly related to polynomials and smooth bump functions, and their topological and geometrical properties are therefore worth studying. In this note we consider the questio[...]![]()
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Azagra Rueda, Daniel ; Fry, Robb ; Montesinos Matilla, Luis Alejandro | America Mathematical Society | 2004-10-21We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have C-p-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y boolean AND U [...]![]()
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We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold M. We give some applications of this theory, concerning, for instance, a Borwein-Preiss type variational principle on a Rie[...]