Search results for "spaces"
showing 10 items of 425 documents
The probability that $x$ and $y$ commute in a compact group
2010
We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…
Vector-valued sequences and multipliers
2015
El texto que se presenta trata de establecer un marco teórico en el que poder manejar dos nuevos conceptos (extensión de conceptos ya conocidos): los multiplicadores por coeficientes a través de una aplicación bilineal y el producto proyectivo tensorial de Hadamard. Ambos espacios se ven siempre como espacios de sucesiones a valores vectoriales, esto es, en un espacio de Banach cualquiera. Posteriormente, se estudia la relación entre ellos y se aportan algunos ejemplos. El punto de partida del proyecto son las clases de espacios introducidas por O.Blasco y M. Pavlovic en el trabajo "Coefficient multipliers on spaces of analytic functions" (Revista Mat. Iberoamericana, 2011) donde se formali…
Norm estimates for operators from Hp to ℓq
AbstractWe give upper and lower estimates of the norm of a bounded linear operator from the Hardy space Hp to ℓq in terms of the norm of the rows and the columns of its associated matrix in certain vector-valued sequence spaces.
Hardy spaces and quasiconformal maps in the Heisenberg group
2023
We define Hardy spaces $H^p$, $00$ such that every $K$-quasiconformal map $f:B \to f(B) \subset \mathbb{H}^1$ belongs to $H^p$ for all $0<p<p_0(K)$. Second, we give two equivalent conditions for the $H^p$ membership of a quasiconformal map $f$, one in terms of the radial limits of $f$, and one using a nontangential maximal function of $f$. As an application, we characterize Carleson measures on $B$ via integral inequalities for quasiconformal mappings on $B$ and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from $\mathbb{R}^n$ to $\mathbb{H}^1$. A crucial difference between the proofs in $\mathbb{R}^n$ and $\mathbb{…
Wilson Loop Form Factors: A New Duality
2017
We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analyti…
Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space
2002
AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.
Entités fonctionnelles, entités spatiales et dynamique urbaine dans la longue durée
2004
Functional Features, spatial Features and the urban Dynamic across a long Lapse of Time. Heterogeneous data from different sources are to be formalised as functional and spatial features in order to study the spatial evolution of preindustrial cities in the « longue durée ». The aim is to establish a distinction between historically relevant functional features and geographically relevant spatial features in order to produce information better adjusted to study spatial dynamics. The elements of a methodology are brought up.
El precio de ser itinerante. Viajes, acompañamiento y espacios cortesanos de la reina Leonor de Sicilia (r. 1349-1375)
2021
This article is an attempt to detail which logistical, economic and human implications had the itinerancy of the medieval monarchy. For this reason, the paper focuses on the characteristics of the itinerancy of Eleanor of Sicily, third wife of Pedro the Ceremonious and queen of the Crown of Aragon between 1349 and 1375. Through the analysis of her documentation, from chancery and treasury resources, it has been possible to establish an itinerary of the queen for three years, from 1354 to 1357. The analysis of this itinerary allows us to see the confluence of the royal couple entourages and the consequences of the beginning of the Dos Pedros war. At the same time, the paper focuses on the pe…
Una Comunità di Chatbot per i Beni Culturali
2005
L'intuizione occupa un ruolo fondamentale nella capacità di ragionamento degli esseri umani. L'obiettivo del lavoro è la progettazione di un'infrastruttura in grado di fornire informazioni che oltre ad appoggiarsi ad un insieme di conoscenze basato su regole sia dotata anche di capacità intuitive. A tal fine è presentato un sistema preliminare che rappresenta il primo passo verso la realizzazione di tale infrastruttura. Il sistema permette ad un utente di interagire con una comunità di chat-bot aventi competenze specifiche in modo da navigare in uno spazio concettuale generato automaticamente con il paradigma di analisi della semantica latente (LSA). La base di conoscenza di ciascun chat-bo…
On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points
2013
In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.