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Tesis Doctoral
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
Invariant subspaces of parabolic self-maps in the Hardy space
(International Press, 2010-01)
It is shown that the lattice of invariant subspaces of the operator of multiplication by a cyclic element of a Banach algebra consists of the closed ideals of this algebra. As an application, with the help of some elements ...
Artículo
A Paley-Wiener theorem for Bergman spaces with application to invariant subspaces
(London Mathematical Society, 2007-06)
An analogue of the Paley–Wiener theorem is developed for weighted Bergman spaces of analytic functions in the upper half-plane. The result is applied to show that the invariant subspaces of the shift operator on the ...
Tesis Doctoral
Funciones universales para operadores de composición en superficies de Riemann
(1994)
"Esta memoria está dividida en cuatro capítulos. En el Capítulo cero de preliminares introducimos la notación y recordamos los elementos necesarios que utilizaremos más tarde en el resto de este trabajo. De este capítulo ...
Artículo
Perron-Frobenius operators and the Klein-Gordon equation
(European Mathematical Society, 2014)
For a smooth curve Γ and a set Λ in the plane R2, let AC(Γ; Λ) be the space of finite Borel measures in the plane supported on Γ, absolutely continuous with respect to the arc length and whose Fourier transform vanishes ...
Artículo
A Birkhoff theorem for Riemann surfaces
(Rocky Mountain Mathematics Consortium, 1998)
A classical theorem of Birkhoff asserts that there exists an entire function f such that the sequence of function {/(z + n)}n≥o is dense in the space of entire functions. In this paper we give sufficient conditions on a ...
Artículo
The Klein–Gordon equation, the Hilbert transform, and dynamics of Gauss-type maps
(European Mathematical Society, 2020)
We study the uncertainty principle associated with the Klein–Gordon equation. As in the previous work [Ann. of Math. 173 (2011)], we consider vanishing along a lattice-cross. The following variants appear naturally: (1) ...
Tesis Doctoral
Artículo
Heisenberg uniqueness pairs and the Klein-Gordon equation
(Princeton University, 2011)
A Heisenberg uniqueness pair (HUP) is a pair (Γ, Λ), where Γ is a curve in the plane and Λ is a set in the plane, with the following property: any bounded Borel measure µ in the plane supported on Γ, which is absolutely ...