Orthogonal series and limit theorems for canonical $U$- and $V$-statistics of stationary connected observations

The limit behavior is studied for the distributions of normalized $U$- and $V$-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying $\varphi$-or $\alpha$-mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix.