Convolution filters for triangles (Q2871642)

The main subject of this article is the convolution product of two triangles. The author constructs a new triangle by erecting similar ears on the sides of a given triangle. He uses the discrete Fourier transformation for triangles and a shape function to give a description of such convolution filters and their iterates.NEWLINENEWLINEWith the aid of the spectral decomposition in the Fourier base of \(\mathbb C^3\) the author represents any triangle of the complex plane as the sum of its centroid and two positively and negatively oriented equilateral triangles.