Dynamics of the heat semigroup in Jacobi analysis

Let $\Delta$ be the Jacobi Laplacian. We study the chaotic and hypercyclic behaviour of the strongly continuous semigroups of operators generated by perturbations of $\Delta$ with a multiple of the identity on $L^p$ spaces

Paley--Wiener Theorems for the U(n)--spherical transform on the Heisenberg group

We prove several Paley--Wiener-type theorems related to the spherical transform on the Gelfand pair $\big(H_n\rtimes U(n),U(n)\big)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in ${\mathbb R}^2$, we prove that spherical transforms of $U(n)$--invariant functions and distributions with compact support in $H_n$ admit unique entire extensions to ${\mathbb C}^2$, and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations

Uniformly bounded representations and completely bounded multipliers of SL(2,R)

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal

“Homo Europaeus"? A comparative analysis of advertising

The narrative repertoire of advertising is the only place where producer and consumer, sender and receiver negotiate a common identity format. The analysis of advertising in European countries shows that there is no such thing as the homo europaeus, but that there are two major continental blocks: the Nort-European one, with its monochronic advertisements, narrative formats based on relationships and soft-sell brand representation mechanisms, in which the context is more relevant than the product itself; in Southern Europe, on the other hand, we found polychronic advertising, narrative formats based on the idea of performance and mechanisms of representation of individual hard-sell products, in which the context loses its prominence

Analisi di Fourier sferica su estensioni risolubili di gruppi di Heisenberg generalizzati

Dottorato di ricerca in matematica. 7. ciclo. A.a. 1991-95. Relatore F. Ricci. Coordinatore F. ArzarelloConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

The Helgason Fourier transform on a class of nonsymmetric harmonic spaces

Given a group N of Heisenberg type, we consider a one-dimensional solvable extension NA of TV, equipped with the natural left-invariant Riemannian metric, which makes NA a harmonic (not necessarily symmetric) manifold. We define a Fourier transform for compactly supported smooth functions on NA, which, when NA is a symmetric space of rank one, reduces to the Helgason Fourier transform. The corresponding inversion formula and Plancherel Theorem are obtained. For radial functions, the Fourier transform reduces to the spherical transform considered by E. Damek and F. Ricci. 1

Paley\u2013Wiener theorems for the U(n)-spherical transform on the Heisenberg group

We prove several Paley\u2013Wiener-type theorems related to the spherical transform on the Gelfand pair H_n xU(n), U(n) , where H_n is the 2n + 1-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in R^2, we prove that spherical transforms of U(n)-invariant functions and distributions with compact support in H_n admit unique entire extensions to C^2 , and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations

GELFAND PAIRS ON THE HEISENBERG GROUP AND SCHWARTZ FUNCTIONS

Abstract. Let Hn be the (2n + 1)–dimensional Heisenberg group and K a compact group of automorphisms of Hn such that (K ⋉Hn, K) is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of K–invariant Schwartz functions on Hn and the space of Schwartz function on a closed subset of Rs homeomorphic to the Gelfand spectrum of the Banach algebra of K–invariant integrable functions on Hn. 1