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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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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