  In this article, we study functional analytic properties of the meromorphic
families of distributions $(\prod_{i=1}^p
(f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p) \in \mathbb{C}^p}$ using
Hironaka's resolution of singularities, then using recent works on the
decomposition of meromorphic germs with linear poles, we renormalize products
of powers of analytic functions $\prod_{i=1}^p(f_j+i0)^{k_j}, k_j \in
\mathbb{Z}$ in the space of distributions. We also study microlocal properties
of $(\prod_{i=1}^p
(f_j+i0)^{\lambda_j})_{(\lambda_1,\dots,\lambda_p)\in\mathbb{C}^p}$ and
$\prod_{i=1}^p (f_j+i0)^{k_j}, k_j \in \mathbb{Z}$. In the second part, we
argue that the above families of distributions with \emph{regular holonomic
singularities} provide a universal model describing singularities of Feynman
amplitudes and give a new proof of renormalizability of quantum field theory on
convex analytic Lorentzian spacetimes as applications of ideas from the first
part.
