  Transfer operators are conjectural "operators of functoriality," which
transfer test measures and (relative) characters from one homogeneous space to
another. In previous work, I computed transfer operators associated to
spherical varieties of rank one, and gave an interpretation of them in terms of
geometric quantization. In this paper, I study how these operators vary in the
horospherical limits of these varieties, where they have a conceptual
interpretation related to scattering theory. I also revisit Jacquet's Hankel
transform for the Kuznetsov formula, which is related to the functional
equation of the standard L-function of GL(n), and provide an interpretation of
it in terms of quantization.
