Análisis Matemáticohttps://hdl.handle.net/11441/108082019-02-16T02:52:03Z2019-02-16T02:52:03ZLocal distribution of Rademacher series and function spaceshttps://hdl.handle.net/11441/823892019-02-04T08:04:13Z2017-05-01T00:00:00ZLocal distribution of Rademacher series and function spaces
2017-05-01T00:00:00ZAplicación de las trasnformaciones de semejanza a diversos problemas numéricos con matriceshttps://hdl.handle.net/11441/813192019-01-04T11:44:33Z1972-03-01T00:00:00ZAplicación de las trasnformaciones de semejanza a diversos problemas numéricos con matrices
1972-03-01T00:00:00ZKomlós' Theorem and the Fixed Point Property for affine mappingshttps://hdl.handle.net/11441/811112018-12-19T07:53:14Z2018-12-01T00:00:00ZKomlós' Theorem and the Fixed Point Property for affine mappings
Assume that X is a Banach space of measurable functions for which Koml´os’ Theorem holds. We associate to any closed convex bounded subset C of X a coefficient t(C) which attains its minimum value when C is closed for the topology of convergence in measure and we prove some fixed point results for affine Lipschitzian mappings, depending on the value of t(C) ∈ [1, 2] and the value of the Lipschitz constants of the iterates. As a first consequence, for every L < 2, we deduce the existence of fixed points for affine uniformly L-Lipschitzian mappings defined on the closed unit ball of L1[0, 1]. Our main theorem also provides a wide collection of convex closed bounded sets in L
1([0, 1]) and in some other spaces of functions, which satisfy the fixed point property for affine nonexpansive mappings. Furthermore, this property is still
preserved by equivalent renormings when the Banach-Mazur distance is
small enough. In particular, we prove that the failure of the fixed point
property for affine nonexpansive mappings in L1(µ) can only occur in
the extremal case t(C) = 2. Examples are displayed proving that our
fixed point theorem is optimal in terms of the Lipschitz constants and
the coefficient t(C).
2018-12-01T00:00:00ZJohn's ellipsoid and the integral ratio of a log-concave functionhttps://hdl.handle.net/11441/803472018-11-19T12:15:18Z2018-04-01T00:00:00ZJohn's ellipsoid and the integral ratio of a log-concave function
We extend the notion of John’s ellipsoid to the setting of integrable
log-concave functions. This will allow us to define the integral ratio of a
log-concave function, which will extend the notion of volume ratio, and we
will find the log-concave function maximizing the integral ratio. A reverse
functional affine isoperimetric inequality will be given, written in terms of this
integral ratio. This can be viewed as a stability version of the functional affine
isoperimetric inequality.
2018-04-01T00:00:00Z