N ov 2 00 5 FOURIER TRANSFORMS RELATED TO A ROOT SYSTEM OF RANK 1

Simulation of an Airy Beam with Optical Vortex under Fractional Fourier Transforms

First, this study obtained the fields of an Airy beam (AiB) with optical vortex (OV) for a Fourier transform (FT) system and a fractional Fourier transform (fractional FT) system; thereafter, their intensity and phase patterns were simulated numerically. The splitting on each line of the phase pattern indicates the position of an OV. The results show that the OV position will change when the po...

1 7 N ov 2 00 4 Cosine Products , Fourier Transforms , and Random Sums ∗

N ov 2 00 3 Fourier - Mukai transforms between canonical divisors , and its application to describing Fourier - Mukai partners

Let X be a smooth 3-fold whose kodaira dimension is positive. The main purpose of this paper is to investigate the set of smooth projective varieties Y whose derived categories of coherent sheaves are equivalent to that of X as triangulated categories. If there exists an equivalence Φ: D(X)→ D(Y ) we can compare derived categories of canonical divisors of X and Y , and this gives an inductive t...

5 N ov 2 00 1 Reductions of N - wave interactions related to low – rank simple Lie algebras . I : Z 2 – reductions

The analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem. We show how the second order reductions of the N–wave interactions related to low–rank simple Lie algebras g can be embedded also in the Weyl group of g. This allows us to display along with the well known ones a number o...

ar X iv : 0 80 5 . 19 18 v 1 [ m at h . C A ] 1 3 M ay 2 00 8 Fourier transform and related integral transforms in superspace

In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the fermionic part of the Fourier kernel has a natural symplectic structure, derived using a Clifford analysis approach. Several basic properties of these three transfor...