  This paper investigates d-dimensional CFTs in the presence of a
codimension-one boundary and CFTs defined on real projective space RP^d. Our
analysis expands on the alpha space method recently proposed for
one-dimensional CFTs in arXiv:1702.08471. In this work we establish integral
representations for scalar two-point functions in boundary and crosscap CFTs
using plane-wave-normalizable eigenfunctions of different conformal Casimir
operators. CFT consistency conditions imply integral equations for the spectral
densities appearing in these decompositions, and we study the relevant integral
kernels in detail. As a corollary, we find that both the boundary and crosscap
kernels can be identified with special limits of the d=1 crossing kernel.
