L^p-summability of Riesz means for the sublaplacian on complex spheres

In this paper we study the L^p-convergence of the Riesz means for the sublaplacian on the sphere S^{2n-1} in the complex n-dimensional space C^n. We show that the Riesz means of order delta of a function f converge to f in L^p(S^{2n-1}) when delta>delta(p):=(2n-1)|1\2-1\p|. The index delta(p) improves the one found by Alexopoulos and Lohoue', 2n|1\2-1\p|, and it coincides with the one found by Mauceri and, with different methods, by Mueller in the case of sublaplacian on the Heisenberg group.Comment: Rapporto interno Politecnico di Torino, Novembre 200

Stability analysis of 5D gravitational solutions with N bulk scalar fields

We study the stability of 5D gravitational solutions containing an arbitrary number of scalar fields. A closed set of equations is derived which governs the background and perturbations of N scalar fields and the metric, for arbitrary bulk and boundary scalar potentials. In particular the effect of the energy-momentum tensor of the scalar fields on the geometry is fully taken into account, together with all the perturbations of the system. The equations are explicitly written as an eigenvalue problem, which can be readily solved to determine the stability of the system and obtain the properties of the fluctuations, such as masses and couplings. As an example, we study a dynamical soft-wall model with two bulk scalar fields used to model the hadron spectrum of QCD and the Higgs sector of electroweak physics. It is shown that there are no tachyonic modes, and that there is a (radion) mode whose mass is suppressed by a large logarithm compared to that of the other Kaluza-Klein modes.Comment: 15 pages, 5 figures. v2: refs adde

Completeness on the worm domain and the M\"untz-Sz\'asz problem for the Bergman space

In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain $\mathcal{W}_\mu$ and its truncated version $\mathcal{W}'_\mu$. We determine some orthogonal systems and show that they are not complete, while showing that the union of two particular of such systems is complete. In order to prove our completeness result we introduce the Muentz-Szasz problem for the 1-dimensional Bergman space of the disk $\{\zeta : |\zeta-1|<1\}$ and find a sufficient condition for its solution.Comment: 14 pages, Author Accepted Manuscrip