  A new class of univariate stationary interpolatory subdivision schemes of
dual type is presented. As opposed to classical primal interpolatory schemes,
these new schemes have masks with an even number of elements and are not
step-wise interpolants. A complete algebraic characterization, which covers
every arity, is given in terms of identities of trigonometric polynomials
associated to the schemes. This characterization is based on a necessary
condition for refinable functions to have prescribed values at the nodes of a
uniform lattice, as a consequence of the Poisson summation formula. A strategy
for the construction is then showed, alongside meaningful examples for
applications that have comparable or even superior properties, in terms of
regularity, length of the support and/or polynomial reproduction, with respect
to the primal counterparts.
