Geodesic
Helly's Theorem and shifts of sets. II. Support function, exponential systems, entire functions
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 122-134

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Let $\mathcal S$ be a family of sets in $\mathbb R^n$, $S$ be the union of all these sets and $C$ be a convex set in $\mathbb R^n$. 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 the 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.
Keywords: convex set, system of linear inequalities, shift, support function, incompleteness of exponential systems, indicator of entire function. 
B. N. Khabibullin. Helly's Theorem and shifts of sets. II. Support function, exponential systems, entire functions. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 122-134. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a9/
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