Geodesic
Completeness criteria of an exponential system in geometric terms of breadth in the direction
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 150-159

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In this paper, we establish criterions for the completeness of an exponential system in spaces of functions that are continuous on a convex compact set and holomorphic in the interior of this compact set and in spaces of holomorphic functions in a convex domain in terms of the directional width of a compact set or a domain. The main results are formulated exclusively in terms of the relationship between the breadth in the direction or the diameter of a compact set or a domain, on the one hand, and the so-called logarithmic submeasures or logarithmic block densities of the distribution of exponential system indicators, on the other hand.
Keywords: completeness of systems of functions, exponential system, breadth in the direction, diameter, entire function of exponential type, distribution of roots, support function. 
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     author = {B. N. Khabibullin and E. G. Kudasheva and A. E. Salimova},
     title = {Completeness criteria of an exponential system in geometric terms of breadth in the direction},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {150--159},
     publisher = {mathdoc},
     volume = {225},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_225_a12/}
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B. N. Khabibullin; E. G. Kudasheva; A. E. Salimova. Completeness criteria of an exponential system in geometric terms of breadth in the direction. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 150-159. http://geodesic.mathdoc.fr/item/INTO_2023_225_a12/