  The structure of exponential subspaces of finitely generated shift-invariant
spaces is well understood and the role of such subspaces for the approximation
power of refinable function vectors and related multi-wavelets is well studied.
In this paper, in the univariate setting, we characterize all analytic
subspaces of finitely generated shift-invariant spaces and provide explicit
descriptions of elements of such subspaces. Consequently, we depict the
analytic functions generated by level dependent (non-stationary) subdivision
schemes with masks of unbounded support. And we confirm the belief that the
exponential polynomials are indeed the only analytic functions generated by
such subdivision schemes with finitely supported masks.
