  We introduce analytic functionals which act on the crossing equation for CFTs
in arbitrary spacetime dimension. The functionals fully probe the constraints
of crossing symmetry on the first sheet, and are in particular sensitive to the
OPE, (double) lightcone and Regge limits. Compatibility with the crossing
equation imposes constraints on the functional kernels which we study in
detail. We then introduce two simple classes of functionals. The first class
has a simple action on generalized free fields and their deformations and can
be used to bootstrap AdS contact interactions in general dimension. The second
class is obtained by tensoring holomorphic and antiholomorphic copies of $d=1$
functionals which have been considered recently. They are dual to simple
solutions to crossing in $d=2$ which include the energy correlator of the Ising
model. We show how these functionals lead to optimal bounds on the OPE density
of $d=2$ CFTs and argue that they provide an equivalent rewriting of the $d=2$
crossing equation which is better suited for numeric computations than current
approaches.
