Completeness of exponential systemsin function spaces in terms of area

B. N. Khabibullin ; E. G. Kudasheva

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 107-117.

Résumé

In this paper, we establish completeness conditions for exponential systems in spaces of functions that are continuous on a compact set with connected complement and holomorphic inside this compact set, in spaces of holomorphic functions in a bounded simply connected domain in terms of the Euclidean area of the convex hull of this compact set or a domain and in terms of some special characteristics or distribution densities of the exponents of the exponential system.

Détail

Keywords: completeness, exponential system, Euclidean area, convex hull, support function, entire function of exponential type, root distribution

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