  A family of regularization functionals is said to admit a linear representer
theorem if every member of the family admits minimizers that lie in a fixed
finite dimensional subspace. A recent characterization states that a general
class of regularization functionals with differentiable regularizer admits a
linear representer theorem if and only if the regularization term is a
non-decreasing function of the norm. In this report, we improve over such
result by replacing the differentiability assumption with lower semi-continuity
and deriving a proof that is independent of the dimensionality of the space.
