Ondřej Kajínek

Generalizing convolution to orbits of Weyl groups of rank 2

Weyl group orbit functions provide generalization of common cosine, sine and exponential functions which are used for generalization of goniometric transforms. Convolution theorem uses goniometric transform to map convolution into multiplication. Generalized transforms give us the chance to explore different types of orbit convolution theorems and orbit convolutions themselves. We present three types of orbit convolutions and related orbit convolution theorems. We show several results of image filtering using orbit convolution as a demonstration of its possibilities.