Composition in Reproducing Kernel Hilbert Spaces à Rebours

This is a recapitulation of the talk (under the same title) designated for IWOTA2022 Session 21 “Truncated and Full Moment Problems, and Applications”. Roughly, the content of this paper provides us with building up the univocal treatment of extending positive definiteness forward and backward. The paper is completed with exposing vital facts (in two Appendices) concerning reproducing kernel Hilbert spaces, the main ingredient of it.