  In this paper, the asymptotic distributions of estimators for the regularized
functional canonical correlation and variates of the population are derived.
The method is based on the possibility of expressing these regularized
quantities as the maximum eigenvalue and the corresponding eigenfunctions of an
associated pair of regularized operators, similar to the Euclidean case. The
known weak convergence of the sample covariance operator, coupled with a
delta-method for analytic functions of covariance operators, yields the weak
convergence of the pair of associated operators. From the latter weak
convergence, the limiting distributions of the canonical quantities of interest
can be derived with the help of some further perturbation theory.
