In the 6-volume ["Generalized functions"](https://bookstore.ams.org/chelgelfset/) a treatment of Fantappie transformations is promised in Vol. 1  (bottom of p.461 of the Russian edition) to come in Vol. 5. However, there is no Fantappie
anywhere in Vol. 5.


A Fantappie transformation is an integral transform
$$
\mu\mapsto\int_{\mathbb{R}^n} \frac{d\mu(X)}{(1-\langle T,X\rangle)^{d+1}}
$$

Does anyone have an idea why the plan was changed? 

My interest in this topic stems from not so well-known fact that certain Fantappie transforms of uniform measures supported on polyhedra are [rational functions of $T$](https://arxiv.org/abs/1210.3193).