On positive definiteness and reproducing spaces

This work examines the structure of positive-definite kernels and their corresponding reproducing spaces. This is done, mainly, by studying certain partial isometries on function spaces. Integral of vector vauled functions is defined on a class of functions which is larger than the class of Bochner measurable functions and smaller than the class of weakly measurable functions. This, together with a detailed study of tensor products of reproducing spaces, yields classical as well as new results for the structure of the cone of positive definite kernels.