In this paper we introduce convolution theorem for the Fourier transform (FT) of two complex functions. We show that the correlation theorem for the FT can be derived using properties of convolution. We develop this idea to derive the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternion functions.
We provide an iterated function system on any compact connected m-dimensional m with just three diffeomorphisms which are C 1-robustly minimal. This improves the main of [Ghane et al., 2010].
This work is devoted to the study of the strong minimality of a class of iterated function systems defined on the two dimensional torus T 2. This means that almost every orbital branch of each point is dense in the ambient space. Moreover, we prove that this property is robust under small perturbations of the generators.
In this article, we study statistical attractors of skew products which have an m-dime compact manifold M as a fiber and their ε-invisible subsets. For any n ≥ 100 m 2 , m = di we construct a set R n in the space of skew products over the horseshoe with the fiber M the following properties. Each C 2-skew product from R n possesses a statistical attracto an… (More)