Oversampling in shift-invariant spaces with a rational sampling period

8 pages, no figures.It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.This work has been supported by the Grant MTM2009-08345 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología

La inculturación del matrimonio en la moderna Jurisprudencia Rotal.

Material incluido en el volumen especial de la revista del Instituto Martín de Azpilcueta, Universidad de Navarra : Ius Canonicum (1999), en honor de Javier Hervada

A normal metal tunnel-junction heat diode

We propose a low-temperature thermal rectifier consisting of a chain of three tunnel-coupled normal metal electrodes. We show that a large heat rectification is achievable if the thermal symmetry of the structure is broken and the central island can release energy to the phonon bath. The performance of the device is theoretically analyzed and, under the appropriate conditions, temperature differences up to $\sim$ 200 mK between the forward and reverse thermal bias configurations are obtained below 1 K, corresponding to a rectification ratio $\mathcal{R} \sim$ 2000. The simplicity intrinsic to its design joined with the insensitivity to magnetic fields make our device potentially attractive as a fundamental building block in solid-state thermal nanocircuits and in general-purpose cryogenic electronic applications requiring energy management.Comment: 4.5 pages, 4 color figure