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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{INTO_2023_225_a12,
     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/}
}
TY  - JOUR
AU  - B. N. Khabibullin
AU  - E. G. Kudasheva
AU  - A. E. Salimova
TI  - Completeness criteria of an exponential system in geometric terms of breadth in the direction
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 150
EP  - 159
VL  - 225
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_225_a12/
LA  - ru
ID  - INTO_2023_225_a12
ER  - 
%0 Journal Article
%A B. N. Khabibullin
%A E. G. Kudasheva
%A A. E. Salimova
%T Completeness criteria of an exponential system in geometric terms of breadth in the direction
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 150-159
%V 225
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_225_a12/
%G ru
%F INTO_2023_225_a12
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/

[1] Bonnezen T., Fenkhel V., Teoriya vypuklykh tel, Fazis, M., 2002

[2] Karimov M. R., Khabibullin B. N., “Sovpadenie nekotorykh plotnostei raspredeleniya mnozhestv i polnota sistem tselykh funktsii”, Tr. Mezhdunar. konf. «Kompleksnyi analiz, differentsialnye uravneniya i smezhnye voprosy. III. Analiz i differentsialnye uravneniya», In-t mat. s vychisl. tsentrom UNTs RAN, Ufa, 2000, 29–34

[3] Krasichkov-Ternovskii I. F., “Interpretatsiya teoremy Berlinga—Malyavena o radiuse polnoty”, Mat. sb., 180:3 (1989), 397–423 | Zbl

[4] Krivosheev A. S., Kuzhaev A. F., “Ob odnoi teoreme Leonteva—Levina”, Ufim. mat. zh., 9:3 (2017), 89–101 | Zbl

[5] Kuzhaev A. F., Rafikov A. I., Krivosheeva O. A., “Ob odnom sootnoshenii dlya logarifmicheskoi blok-plotnosti”, Vestn. Bashkir. un-ta., 22:1 (2017), 25–27

[6] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Fizmatgiz, M., 1956

[7] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR

[8] Leontev A. F., Ryady eksponent, Nauka, M., 1978 | MR

[9] Magaril-Ilyaev G. G., Tikhomirov V. M., Vypuklyi analiz i ego prilozheniya, Editorial URSS, M., 2000

[10] Rokafellar R. T., Vypuklyi analiz, Mir, M., 1973

[11] Salimova A. E., Khabibullin B. N., “Rost subgarmonicheskikh funktsii vdol pryamoi i raspredelenie ikh mer Rissa”, Ufim. mat. zh., 12:2 (2020), 35–48 | MR | Zbl

[12] Salimova A. E., Khabibullin B. N., “Raspredelenie nulei tselykh funktsii eksponentsialnogo tipa s ogranicheniyami na rost vdol pryamoi”, Mat. zametki., 108:4 (2020), 588–600 | DOI | MR | Zbl

[13] Salimova A. E., Khabibullin B. N., “Rost tselykh funktsii eksponentsialnogo tipa i kharakteristiki raspredelenii tochek vdol pryamoi na kompleksnoi ploskosti”, Ufim. mat. zh., 13:3 (2021), 116–128 | MR | Zbl

[14] Santalo L., Integralnaya geometriya i geometricheskie veroyatnosti, Nauka, M., 1983

[15] Tikhomirov V. M., “Vypuklyi analiz”, Itogi nauki tekhn. Ser. Sovr. probl. mat. Fundam. napravl., 14 (1987), 5–101

[16] Khabibullin B. N., “O malosti rosta na mnimoi osi tselykh funktsii eksponentsialnogo tipa s zadannymi nulyami”, Mat. zametki., 43:5 (1988), 644–650 | MR

[17] Khabibullin B. N., “O roste tselykh funktsii eksponentsialnogo tipa vdol mnimoi osi”, Dokl. AN SSSR., 302:2 (1988), 270–273

[18] Khabibullin B. N., “O roste tselykh funktsii eksponentsialnogo tipa vdol mnimoi osi”, Mat. sb., 180:5 (1989), 706–719 | Zbl

[19] Khabibullin B. N., “O roste tselykh funktsii eksponentsialnogo tipa s zadannymi nulyami vdol pryamoi”, Anal. Math., 17:3 (1991), 239–256 | DOI | MR | Zbl

[20] Khabibullin B. N., “Nekonstruktivnye dokazatelstva teoremy Berlinga—Malyavena o radiuse polnoty i teoremy needinstvennosti dlya tselykh funktsii”, Izv. RAN. Ser. mat., 58:4 (1994), 125–148 | Zbl

[21] Khabibullin B. N., “Posledovatelnost nulei golomorfnykh funktsii, predstavlenie meromorfnykh funktsii. II. Tselye funktsii”, Mat. sb., 200:2 (2009), 129–-158 | DOI | Zbl

[22] Khabibullin B. N., Polnota sistem eksponent i mnozhestva edinstvennosti, Ufa, 2012

[23] Khabibullin B. N., “Teorema Khelli i sdvigi mnozhestv. I”, Ufim. mat. zh., 6:3 (2014), 98–111 | MR

[24] Khabibullin B. N., “Teorema Khelli i sdvigi mnozhestv. II. Opornaya funktsiya, sistemy eksponent, tselye funktsii”, Ufim. mat. zh., 6:4 (2014), 125–138 | Zbl

[25] Khabibullin B. N., “Raspredeleniya kornei i mass tselykh i subgarmonicheskikh funktsii s ogranicheniyami na ikh rost vdol polosy”, Izv. RAN. Ser. mat., 88:1 (2024)

[26] Khabibullin B. N., Muryasov R. R., “Geometricheskie usloviya polnoty eksponentsialnykh sistem”, Mat. Mezhdunar. konf. Voronezh. vesennyaya mat. shkola «Pontryaginskie chteniya–XXXIII. Sovremennye metody teorii kraevykh zadach» (Voronezh, 3-9 maya 2022 g.), Voronezh, 2022, 251–253

[27] Khabibullin B. N., Khabibullin F. B., Cherednikova L. Yu., “Podposledovatelnosti nulei dlya klassov golomorfnykh funktsii, ikh ustoichivost i entropiya lineinoi svyaznosti. II”, Algebra i analiz., 20:1 (2008), 190–236

[28] Khadviger G., Lektsii ob ob'eme, ploschadi poverkhnosti i izoperimetrii, Nauka, M., 1966

[29] Khabibullin B. N., The Malliavin–Rubel theorem on small entire functions of exponential type with given zeros: 60 years later, arXiv: https://arxiv.org/abs/2204.11603v1 | MR

[30] Khabibullin B. N., “Distribution of zeros for entire functions”, Proc. Int. Conf. “Complex Analysis and Related Topics” (Kazan, June 30 – July 4, 2022), Kazan, 30–31

[31] Levin B. Ya., Lectures on Entire Functions, Am. Math. Soc., Providence, Rhode Island, 1996 | MR | Zbl

[32] Malliavin P., Rubel L. A., “On small entire functions of exponential type with given zeros”, Bull. Soc. Math. France., 89:2 (1961), 175–201 | DOI | MR

[33] Redheffer R. M., “Completeness of sets of complex exponentials”, Adv. Math., 24 (1977), 1–62 | DOI | MR | Zbl

[34] Rubel L. A., Colliander J. E., Entire and Meromorphic Functions, Springer-Verlag, Berlin, 1996 | MR | Zbl