Abstract
We deal with the Fourier-like analysis of functions on discrete grids in two-dimensional simplexes using C- and E-Weyl group orbit functions. For these cases, we present the convolution theorem. We provide an example of application of image processing using the C-functions and the convolutions for spatial filtering of the treated image.
Highlights
The development of information technologies has inspired the development of the information compression, the most famous part of which is the image and video compression
We summarize the properties of C- and E-orbit functions connected with Weyl groups of simple Lie algebras A2,C2 and G2
There are some restrictions for the orbit convolution coming from its definition, the most significant is the summation over all reflections of the convolution kernel
Summary
The development of information technologies has inspired the development of the information compression, the most famous part of which is the image and video compression. We focus on the simplest non-trivial case of utilization of orbit functions in two dimensions It corresponds to a two-dimensional digital image processing. We summarize the properties of C- and E-orbit functions connected with Weyl groups of simple Lie algebras A2 ,C2 and G2 These functions are a generalization of the classical cosine, sine and exponential function, and they act in fundamental domains of the Lie algebras. In these domains, we introduce a discrete grid on which it is possible to define discrete C- and E-orbit transform.
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