Información del autor
Autor Azagra Rueda, Daniel |
Documentos disponibles escritos por este autor (46)
![](./images/expand_all.gif)
![](./images/collapse_all.gif)
![Selecciones disponibles](./images/orderby_az.gif)
![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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 [...]![]()
texto impreso
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[...]![]()
texto impreso
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 [...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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.![]()
texto impreso
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.![]()
texto impreso
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[...]![]()
texto impreso
![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
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[...]![]()
texto impreso
Let C be a subset of ?n (not necessarily convex), f : C ? R be a function and G : C ? ?n be a uniformly continuous function, with modulus of continuity ?. We provide a necessary and sufficient condition on f, G for the existence of a convex func[...]