X iv :m at h/ 02 10 08 4v 1 [ m at h. C A ] 7 O ct 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon th...

We describe a technique for measuring the surface profile of a radio telescope with a fast paraboloidal primary. The technique uses a sensor, at the center of curvature of the primary, consisting of a millimeter-wave source and an array of receivers to measure the field in the caustic. The sensor is mounted on the telescope enclosure and it moves with the telescope, so the measurements can be u...

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or t...

In this paper we present a shadow mapping technique for hemispherical and omnidirectional light sources using dual-paraboloid mapping. In contrast to the traditional perspective projection this parameterization has the benefit that only a minimal number of rendering passes is needed during generation of the shadow maps, making the method suitable for dynamic environments and real time applicati...

Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) We review the coherent state or group-theoretical construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two-sheeted hyperboloid, emphasizing the similarities between the two cases.. Finally we give some indications on the CWT on a...

It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such solution its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in R: paraboloid, ellips...

We show that, possibly after a compactification of spacetime, constant functions are local maximizers the Tomas-Stein adjoint Fourier restriction inequality for cone and paraboloid in every dimension, sphere dimension up to 60. For we work from PDE framework, which enables use Penrose Lens transformations, map conjectured optimal into constants.