Function spaces for conditionally positive definite operator-valued kernels.

The correspondence between reproducing kernel Hilbert spaces and positive definite kernels is well understood since Aronszajn’s work of the 1940s. The analog relation is less clear for conditionally positive definite kernels. The latter are widely used in approximation methods for scattered data, geostatistics, and machine learning. We consider this relation and provide two ways to construct a reproducing kernel Pontryagin space for operator-valued kernels