  Generalizations and variations of the fundamental lemma by Willems et al. are
an active topic of recent research. In this note, we explore and formalize the
links between kernel regression and known nonlinear extensions of the
fundamental lemma. Applying a transformation to the usual linear equation in
Hankel matrices, we arrive at an alternative implicit kernel representation of
the system trajectories while keeping the requirements on persistency of
excitation. We show that this representation is equivalent to the solution of a
specific kernel regression problem. We explore the possible structures of the
underlying kernel as well as the system classes to which they correspond.
