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Autor Azagra Rueda, Daniel |
Documentos disponibles escritos por este autor (46)
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Let X be a separable Banach space with a separating polynomial. We show that there exists C > = 1 (depending only on X) such that for every Lipschitz function f : X -> R, and every epsilon > 0, there exists a Lipschitz, real analytic function [...]![]()
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We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinite-dimensional Banach space and F is a closed subspace o[...]![]()
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We show how Lasry-Lions's result on regularization of functions defined on R-n or on Hilbert spaces by sup inf convolutions with squares of distances can be extended to (finite or infinite dimensional) Riemannian manifolds M of bounded sectional[...]![]()
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Azagra Rueda, Daniel ; Muñoz-Fernández, Gustavo A. ; Seoane-Sepúlveda, Juan B. ; Sánchez de los Reyes, Víctor Manuel | Academic Press | 2009-06If f is continuous on the interval [a, b], g is Riemann integrable (resp. Lebesgue measurable) on the interval [alpha, beta] and g([alpha, beta]) subset of [a, b], then f o g is Riemann integrable (resp. measurable) on [alpha, beta]. A well-know[...]![]()
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In this note we prove that if a differentiable function oscillates between y« and « on the boundary of the unit ball then there exists a point in the interior of the ball in which the differential of the function has norm equal or less than« . T[...]![]()
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We establish a second order smooth variational principle valid for functions defined on (possibly infinite- dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectiona[...]![]()
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Azagra Rueda, Daniel ; Ferrera Cuesta, Juan ; López-Mesas Colomina, Fernando ; Rangel, Y. | Elsevier | 2007-02-15We show that for every Lipschitz function f defined on a separable Riemannian manifold M (possibly of infinite dimension), for every continuous epsilon : M -> (0, + infinity), and for every positive number r > 0, there exists a C-infinity smoo[...]![]()
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Let X be a Banach space with a separable dual X*. Let Y subset of X be a closed subspace, and f : Y -> R a C(1)-smooth function. Then we show there is a C(1) extension of f to X.![]()
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Let X be an infinite-dimensional Banach space, and let A be a CP Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that.![]()
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This article deals with smooth removability of compact sets in infinite-dimensional Banach spaces. The main result states that ifX is an infinite-dimensional Banach space which has a not necessarily equivalent Cp-smooth norm and K is a compact s[...]![]()
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Two main results presented by the authors include a mean-value inequality for a class of Gateaux subdifferentiable functions and a subdifferential Rolle’s theorem in a Banach space. For the second part, if a (Gateaux/Fréchet)subdifferentiable fu[...]![]()
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We prove the following new characterization of Cp Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a Cp smooth (Lipschitz) bump function if and only if it has another Cp smooth (Lipschitz) bump function f such t[...]![]()
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We prove that every continuous mapping from a separable infinite-dimensional Hilbert space X into R-m can be uniformly approximated by C-infinity-smooth mappings with no critical points. This kind of result can be regarded as a sort of strong ap[...]![]()
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We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F(x, u, du, d(2)u) = 0 defined on a finite-dimensional Riemannian manifold M. Finest res[...]