Marcinkiewicz-Zygmund inequalities and interpolation by spherical harmonics

We find necessary density conditions for Marcinkiewicz-Zygmund inequalities and interpolation for spaces of spherical harmonics with respect to the L^p norm. Moreover, we prove that there are no complete interpolation families for p\neq 2

Com repartir punts uniformement en esferes?

El teorema de WhittakerKotel'nikovShannon permet reconstruir de manera estable una funció de banda limitada i energia finita a partir dels valors de la funció als enters. Així doncs, els enters són un exemple de conjunt de mostreig estable però són, a més, un conjunt de punts ben distribuïts a la recta. En aquest article tractarem de la relació entre l'existència de conjunts de punts ben distribuïts i el mostreig estable de funcions a diferents dominis (la recta, el cercle i l'esfera).How to distribute points uniformly on spheres? The Whittaker-Kotel’nikov-Shannon theorem allows us to recover, in a stable way, a bandlimited function of finite energy by using only its values on the integers. Hence, the integers give an example of a set of stable sampling which is evenly distributed on the real line. In this paper, we consider the relation between the existence of evenly distributed sets of points and sets of stable sampling in various settings (the real line, the circle and the sphere)

Sampling and interpolation in de Branges spaces with doubling phase

The de Branges spaces of entire functions generalise the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterisation, in terms of densities, for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure on the real line. Moreover, a consequence of this doubling condition, is that the spaces we consider are one component model spaces. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and Ortega-Cerd\'a for Fock spaces satisfying a doubling condition analogue to ours.Comment: 31 pages, 1 figur

Printed Circuit Board (PCB) design process and fabrication

This module describes main characteristics of Printed Circuit Boards (PCBs). A brief history of PCBs is introduced in the first chapter. Then, the design processes and the fabrication of PCBs are addressed and finally a study case is presented in the last chapter of the module.Peer ReviewedPostprint (published version