ar X iv : m at h / 07 02 43 6 v 1 [ m at h . N T ] 1 5 Fe b 20 07 Calculation of l - adic Local Fourier Transformations ∗

ar X iv : m at h / 07 02 43 6 v 4 [ m at h . N T ] 4 J ul 2 00 8 Calculation of l - adic Local Fourier Transformations ∗

We calculate the local Fourier transformations for a class of Ql-sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([15] 2.6.3). As an application, we calculate the local monodromy of l-adic hypergeometric sheaves introduced by Katz ([12]). We also discuss the characteristic p analogue of the Turrittin-Levelt Theorem for D-modules. The method used in this paper can be used ...

ar X iv : m at h / 05 02 50 5 v 1 [ m at h . A P ] 2 4 Fe b 20 05 Some Remarks on Strichartz Estimates for Homogeneous Wave Equation ∗

We give several remarks on Strichartz estimates for homogeneous wave equation with special attention to the cases of Lx estimates, radial solutions and initial data from the inhomogeneous Sobolev spaces. In particular, we give the failure of the endpoint estimate L 4 n−1 t Lx for n = 2, 3 even for data in inhomogeneous Sobolev spaces.

ar X iv : m at h / 02 05 20 7 v 1 [ m at h . R T ] 1 9 M ay 2 00 2 Can p - adic integrals be computed ?

This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.

ar X iv : m at h / 05 02 35 7 v 1 [ m at h . N A ] 1 6 Fe b 20 05 A Sublinear Algorithm of Sparse Fourier Transform for Nonequispaced Data ∗

We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L < N are available. If the ratio p = L/N is not close to 1, the available data are typically non-equispaced samples. Then our algorithm reconstructs a near-optimal B-term representation R with high probability 1−...

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities