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. 
@article{UFA_2014_6_4_a9,
     author = {B. N. Khabibullin},
     title = {Helly's {Theorem} and shifts of {sets.~II.} {Support} function, exponential systems, entire functions},
     journal = {Ufa mathematical journal},
     pages = {122--134},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a9/}
}
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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/