  Based on the "generating operator" of the Rankin--Cohen brackets introduced
in Kobayashi-Pevzner [arXiv:2306.16800], we present a method to construct
various fundamental operators with continuous parameters such as invariant
trilinear forms on infinite-dimensional representations, the Fourier and the
Poisson transforms on the anti-de Sitter space, and integral symmetry breaking
operators for the fusion rules, among others, out of a countable set of
differential symmetry breaking operators.
