  Let $Z$ and $W$ are distributions of points on the complex plane $\mathbb C$.
The following problem goes back to the studies of F. Carlson, T. Carleman, L.
Schwartz, A. F. Leont'ev, B. Ya. Levin, J.-P. Kahane and others. For which $Z$
and $W$ for an entire function $g\neq 0$ of exponential type vanishing on $W$,
there is an entire function $f\neq 0$ of exponential type vanishing on $Z$ such
that $|f|\leq |g|$ on the imaginary axis? The classical Malliavin-Rubel theorem
of the early 1960s completely solves this problem for "positive" $Z$ and $W$
lying only on the positive semiaxis. A number of generalizations of this
criterion were established by us in the late 1980s for "complex"
$Z\subset\mathbb C$ and $W\subset\mathbb C$ separated by angles from the
imaginary axis, with some advances in the 2020s. In this paper, tougher
problems are solved in a more general subharmonic framework for distributions
of masses on $\mathbb C$. All the previously mentioned results can be obtained
from the main results of the paper in a much stronger form even in the initial
formulation for distributions of points $Z$ and $W$ and entire functions $f$
and $g$ of exponential type. Some of the results of the article are closely
related to the famous Beurling-Malliavin theorems on the radius of completeness
and the multiplier.
