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Artículo
Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds
(Duke University Press, 2004-07-15)
We prove that every continuous mapping from a separable infinitedimensional Hilbert space X into R m can be uniformly approximated by C∞ smooth mappings with no critical points. This kind of result can be regarded as a ...
Capítulo de Libro
Refined size estimates for Furstenberg sets via Hausdorff measures: a survey of some recent results
(Springer, 2014)
In this survey we collect and discuss some recent results on the so called “Furstenberg set problem”, which in its classical form concerns the estimates of the Hausdorff dimension (dimH) of the sets in the Fα-class: for ...
Artículo
Smooth Lipschitz retractions of starlike bodies onto their boundaries in infinite-dimensional Banach spaces
(London Mathematical Society, 2001)
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 (1) The boundary ∂A is C p Lipschitz contractible. (2) There ...
Artículo
On regularization in superreflexive Banach spaces by infimal convolution formulas
(Polish Academy of Sciences, Institute of Mathematics, 1998)
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-H¨older derivatives (for some 0 < α ≤ 1). The smooth approximation is given by means of ...
Artículo
Approximation of Lipschitz functions by Δ-convex functions in banach spaces
(Springer, 1998-12)
In this paper we give some results about the approximation of a Lipschitz function on a Banach space by means of ∆-convex functions. In particular, we prove that the density of ∆-convex functions in the set of Lipschitz ...
Ponencia
Uniform approximation of continuous functions by smooth functions with no critical points on Hilbert manifolds
(2001)
We prove that every continuous function on a separable infinitedimensional Hilbert space X can be uniformly approximated by C∞ smooth functions with no critical points. This kind of result can be regarded as a sort of ...