Kernel construction techniques

This paper extends a talk at the Conference on Modern Kernel Methods and Applications in Hong Kong Baptist University in January 2026. It first reviews standard kernel constructions, but then goes over to recent extensions and presents many starting points to construct future kernels. The goal of the paper is to encourage readers to go into kernel engineering , in particular towards constructing C ∞ kernels with compact support. The techniques presented here use series expansions, convolution, subdivision, componentwise products and radialization. Most cases are illustrated by examples, but a deeper analysis is left for future research, together with applications.