Given a commuting n-tuple of bounded linear operators on a Hilbert space, together with a distinguished cyclic vector, Jim Agler defined a linear functional on the polynomial ring. ``Near subnormality properties'' of an operator are translated into positivity properties of the linear functional. We approach ``near subnormality properties'' in a different way by answering the following question: when is this linear functional given by a compactly supported distribution? The answer is in terms of the off-diagonal growth condition of a two-variable kernel function. Using the reproducing kernel Hilbert spaces (RKHS) defined by the kernel function, we give a function model for all cyclic commuting n-tuples. This potentially gives a different approach to operator models.