arXiv subjects

A. Bonilla

Publications and source records attributed to A. Bonilla.

6 recordsLinked to original sources

arXiv2023

White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era

The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test, where a clear signal of quantum properties of gravity is still missing. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, as it allows us to study particles with much higher energies and travelling much longer distances than possible in terrestrial experiments, but more progress is needed on several fronts. A thorough appraisal of current strategies and experimental frameworks, regarding quantum gravity phenomenology, is provided here. Our aim is twofold: a description of tentative multimessenger explorations, plus a focus on future detection experiments. As the outlook of the network of researchers that formed through the COST Action CA18108 ``Quantum gravity phenomenology in the multi-messenger approach (QG-MM)'', in this work we give an overview of the desiderata that future theoretical frameworks, observational facilities, and data-sharing policies should satisfy in order to advance the cause of quantum gravity phenomenology.

gr-qc↗

arXiv2019

Kreiss bounded and uniformly Kreiss bounded operators

If $T$ is a Kreiss bounded operator on a Banach space, then $\|T^n\|=O(n)$. Forty years ago Shields conjectured that in Hilbert spaces, $\|T^n\| = O(\sqrt{n})$. A negative answer to this conjecture was given by Spijker, Tracogna and Welfert in 2003. We improve their result and show that this conjecture is not true even for uniformly Kreiss bounded operators. More precisely, for every $\varepsilon>0$ there exists a uniformly Kreiss bounded operator $T$ on a Hilbert space such that $\|T^n\|\sim (n+1)^{1-\varepsilon}$ for all $n\in \Bbb N$. On the other hand, any Kreiss bounded operator on Hilbert spaces satisfies $\|T^n\|=O(\frac{n}{\sqrt{\log n}})$. We also prove that the residual spectrum of a Kreiss bounded operator on a reflexive Banach space is contained in the open unit disc, extending known results for power bounded operators. As a consequence we obtain examples of mean ergodic Hilbert space operators which are not Kreiss bounded.

math.FA↗

arXiv2018

$C_0$-semigroups of $m$-isometries on Hilbert spaces

Let $\{T(t)\}_{t\ge 0}$ be a $C_0$-semigroup on a separable Hilbert space $H$. We characterize that $T(t)$ is an $m$-isometry for every $t$ in terms that the mapping $t\in \Bbb R^+ \rightarrow \|T(t)x\|^2$ is a polynomial of degree less than $m$ for each $x\in H$. This fact is used to study $m$-isometric right translation semigroup on weighted $L^p$-spaces. We characterize the above property in terms of conditions on the infinitesimal generator operator or in terms of the cogenerator operator of $\{ T(t)\}_{t\geq 0}$. Moreover, we prove that a non-unitary $2$-isometry on a Hilbert space satisfying the kernel condition, that is, $$ T^*T(KerT^*)\subset KerT^*\;, $$ then $T$ can be embedded into a $C_0$-semigroup if and only if $dim (KerT^*)=\infty$.

math.FA↗

arXiv2018

Mean Li-Yorke chaos in Banach spaces

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only if it has an absolutely mean irregular vector. As a consequence, absolutely Cesàro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke chaos is shown to be equivalent to the existence of a dense (or residual) set of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a sufficient condition for the existence of a dense absolutely mean irregular manifold are also obtained. Moreover, we construct an example of an invertible hypercyclic operator $T$ such that every nonzero vector is absolutely mean irregular for both $T$ and $T^{-1}$. Several other examples are also presented. Finally, mean Li-Yorke chaos is also investigated for $C_0$-semigroups of operators on Banach spaces.

math.FA↗

arXiv2016

Observación de lentes gravitatorias con ALMA

Gravitational lensing is a fundamental tool for cosmology. A recent instrument which will provide more information for models of these objects is ALMA. Our goal is to select lens candidates to observe with ALMA and then model them using GravLens Software. We had selected 12 quadruple images systems from the CASTLES database, which show a high probability of observing extended sources in the submillimetric range. These new data will allow us to improve existing models. Las lentes gravitatorias son una herramienta fundamental para la cosmología. Un nuevo instrumento que nos proporcionará mayor información para los modelos de estos objetos, es ALMA. Nuestro objetivo es seleccionar lentes candidatas para observar con ALMA y posteriormente modelarlas mediante el programa GravLens. Seleccionamos de la base de datos de CASTLES, 12 sistemas cuádruples, los cuales tienen mayor probabilidad de observar fuentes extendidas en el rango submilimétrico. Estos nuevos datos nos permitirán mejorar los modelos exitentes para dichos sistemas.

astro-ph.GA↗

arXiv2014

On convex-cyclic operators

We give a Hahn-Banach Characterization for convex-cyclicity. We also obtain an example of a bounded linear operator $S$ on a Banach space with $σ_{p}(S^*)=\emptyset$ such that $S$ is convex-cyclic, but $S$ is not weakly hypercyclic and $S^2 $ is not convex-cyclic. This solved two questions of Rezaei in \cite{Rezaei} when $σ_p(S^*)=\varnothing$. %Recently, León-Saavedra and Romero de la Rosa \cite{LeRo} provide an example of a convex-cyclic operator $S$ such that the power $S^n$ fails to be convex-cyclic with $σ_p(S^*)\neq \varnothing$. In fact they solved tree questions posed by Rezaei in \cite{Rezaei}. Moreover, we prove that $m$-isometries are not convex-cyclic and that $\varepsilon$-hypercyclic operators are convex-cyclic. We also characterize the diagonalizable normal operators that are convex-cyclic and give a condition on the eigenvalues of an arbitrary operator for it to be convex-cyclic. We show that certain adjoint multiplication operators are convex-cyclic and show that some are convex-cyclic but no convex polynomial of the operator is hypercyclic. Also some adjoint multiplication operators are convex-cyclic but not 1-weakly hypercyclic.

math.FA↗