# Article

Ufa Mathematical Journal
Volume 6, Number 4, pp. 122-134

# Helly's Theorem and shifts of sets. II. Support function, exponential systems, entire functions

Khabibullin B.N.

DOI:10.13108/2014-6-4-122

Let $\mathcal S$ be a family of sets in $\mathds{R}^n$, $S$ be the union of all these sets and $C$ be a convex set in $\mathds{R}^n$. In terms of support functions of sets in $\mathcal S$ and set $C$ we establish necessary and sufficient conditions under which a parallel shift of set $C$ covers set $S$. We study independently the two-dimensional case, when sets are unbounded, by employing additional characteristics of sets. We give applications of these results to the problems of incompleteness of exponential systems in function spaces.