Geodesic
An existence domain of the sum of exponential monomials series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 56-66.

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

In this paper series of exponential monomials are considered. We study conditions on sequences of indexes such that existence domains of the sum of these series coincide with their convergence domains.
Keywords: series of exponential monomials, singular point
Mots-clés : convex domain, convergence domain, existence domain. 
@article{IVM_2021_3_a4,
     author = {O. A. Krivosheeva and A. S. Krivosheev},
     title = {An existence domain of the sum of exponential monomials series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {56--66},
     publisher = {mathdoc},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_3_a4/}
}
TY  - JOUR
AU  - O. A. Krivosheeva
AU  - A. S. Krivosheev
TI  - An existence domain of the sum of exponential monomials series
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 56
EP  - 66
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_3_a4/
LA  - ru
ID  - IVM_2021_3_a4
ER  - 
%0 Journal Article
%A O. A. Krivosheeva
%A A. S. Krivosheev
%T An existence domain of the sum of exponential monomials series
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 56-66
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_3_a4/
%G ru
%F IVM_2021_3_a4
O. A. Krivosheeva; A. S. Krivosheev. An existence domain of the sum of exponential monomials series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2021), pp. 56-66. http://geodesic.mathdoc.fr/item/IVM_2021_3_a4/

[1] Krivosheeva O. A., “Oblast skhodimosti ryadov eksponentsialnykh monomov”, Ufimsk. matem. zhurn., 3:2 (2011), 43–56 | MR

[2] Hadamard J., “Essai sur l'etude des fonctions donnes par leur développement de Taylor”, J. Math. Pures Appl. Ser. (4), 4:8 (1892), 101–106

[3] Fabry E., “Sur les points singuliers d'une function donnée par son développement en série et l'impossibilité du prolongement analytique dans des cas trés généraux”, Ann. Ecole Norm. Sup., 13:3 (1896), 367–399 | DOI | MR | Zbl

[4] Pólya J., “Über die Existenz unendlich vieler singulärer Punkte auf der Konvergenzgeraden gewisser Dirichletscher Reihen”, Sitzungber. Preuss. Akad. Wiss., Phys.-Math. Kl., 1923, 45–50 | Zbl

[5] Pólya J., “Eine Verallgemeinerung des Fabryschen Luc̈kensatzes”, Nachr. Ges. Wiss. Gottingen, Math.-Phys. Kl., 2 (1927), 187–195

[6] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[7] Bernstein V., Leçons sur les progréss récents de la théorie des séries de Dirichlet, Gauthier-Villars, Paris, 1933

[8] Leontev A. F., Tselye funktsii. Ryady eksponent, Nauka, M., 1983

[9] Krivosheeva O. A., “Osobye tochki summy ryada eksponentsialnykh monomov na granitse oblasti skhodimosti”, Algebra i analiz, 23:2 (2011), 162–205 | MR

[10] Krivosheev A. S., “Fundamentalnyi printsip dlya invariantnykh podprostranstv v vypuklykh oblastyakh”, Izv. RAN. Ser. matem., 68:2 (2004), 71–136 | MR | Zbl

[11] Krivosheeva O. A., Krivosheev A. S., “Kriterii vypolneniya fundamentalnogo printsipa dlya invariantnykh podprostranstv v ogranichennykh vypuklykh oblastyakh kompleksnoi ploskosti”, Funkts. analiz i ego prilozh., 46:4 (2012), 14–30 | MR | Zbl

[12] Zikkos E., “A Taylor-Dirichlet series with no singularities on its abscissa of convergence”, Ufimsk. matem. zhurn., 10:3 (2018), 146–152 | MR | Zbl

[13] Krivosheev A. S., Krivosheeva O. A., “Raspredelenie osobykh tochek summy ryada eksponentsialnykh monomov na granitse oblasti skhodimosti”, Matem. sb., 211:1 (2020), 55–114 | MR | Zbl

[14] Pólya J., “Untersuchungen uber Lucken und Singularitaten von potenzreihen”, Math. Z., 29 (1929), 549–640 | DOI | MR | Zbl

[15] Koosis P., The Logarithmic Integral, v. 1, Cambridge University Press, Cambridge, 1997 | MR

[16] Kondratyuk A. A., “Tselye funktsii s konechnoi maksimalnoi plotnostyu nulei. I”, Teoriya funktsii, funkts. analiz i ikh prilozh., 10 (1970), 56–70

[17] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[18] Krivosheev A. S., Krivosheeva O. A., “Fundamentalnyi printsip i bazis v invariantnom podprostranstve”, Matem. zametki, 99:5 (2016), 684–697 | MR | Zbl

[19] Abdulnagimov A. I., Krivosheev A. S., “Pravilno raspredelennye podmnozhestva v kompleksnoi ploskosti”, Algebra i analiz, 28:4 (2016), 1–46 | MR