Málstofa í stærðfræði
Speaker: Christer O. Kiselman, Uppsala University
Title: Discrete convolution operators, the Fourier transformation, and its tropical counterpart: the Fenchel transformation
Staðsetning: Naustið, Endurmenntun (hér)
Tími: Þriðjudagur 26. maí, klukkan 15:00-16:00.
We study solvability of convolution equations for functions with discrete support in \(mathbb R^n\), a special case being functions with support in the integer points. The more general case is of interest for several grids in Euclidean space, like the body-centered and face-centered tesselations of three-space.
The theorem of existence of fundamental solutions by Boor, Höllig & Riemenschneider is generalized to general discrete supports using only elementary methods. We also study the asymptotic growth of sequences and arrays using the Fourier and Fenchel transformations.