Geodesic
Continuation of Functions Representable via Infinitely Multiple Exponentials with Alternating Exponents
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 163-172 
G. A. Ambartsumian; A. V. Burobin. Continuation of Functions Representable via Infinitely Multiple Exponentials with Alternating Exponents. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 163-172. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a0/
@article{MZM_2003_73_2_a0,
     author = {G. A. Ambartsumian and A. V. Burobin},
     title = {Continuation of {Functions} {Representable} via {Infinitely} {Multiple} {Exponentials} with {Alternating} {Exponents}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--172},
     year = {2003},
     volume = {73},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a0/}
}
TY  - JOUR
AU  - G. A. Ambartsumian
AU  - A. V. Burobin
TI  - Continuation of Functions Representable via Infinitely Multiple Exponentials with Alternating Exponents
JO  - Matematičeskie zametki
PY  - 2003
SP  - 163
EP  - 172
VL  - 73
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a0/
LA  - ru
ID  - MZM_2003_73_2_a0
ER  - 
%0 Journal Article
%A G. A. Ambartsumian
%A A. V. Burobin
%T Continuation of Functions Representable via Infinitely Multiple Exponentials with Alternating Exponents
%J Matematičeskie zametki
%D 2003
%P 163-172
%V 73
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a0/
%G ru
%F MZM_2003_73_2_a0

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

For infinitely multiple exponentials with two alternating exponents, we construct continuations to unbounded domains, so that these continuations are the limit functions of sequences of finitely multiple exponentials. We prove that, for different exponents, such a continuation is unique in the class of continuously differentiable functions. We extend the domain of existence of infinitely multiple exponentials. For exponents with the same signs, this domain remains bounded, while for exponents with different signs, it coincides with the number axis.

[1] Bulanov A. P., “Regulyarnost stepenei beskonechnoi kratnosti”, Izv. RAN. Ser. matem., 62:5 (1998), 49–78 | MR | Zbl

[2] Knoebel A., “Exponentials reiterated”, Amer. Math. Monthly, 88:4 (1981), 235–252 | DOI | MR | Zbl

[3] Bulanov A. P., “O stepeni beskonechnoi kratnosti s koeffitsientami, imeyuschimi poocheredno dva znacheniya”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tezisy dokladov 9-i Saratovskoi zimnei shkoly, Izd-vo Saratovskogo un-ta, Saratov, 1998, 31

[4] Ambartsumyan G. A., Burobin A. V., “O prodolzhenii funktsii, predstavlyaemykh eksponentami beskonechnoi kratnosti”, Sovremennye metody teorii funktsii i smezhnye problemy, Tezisy dokladov Voronezhskoi zimnei matematicheskoi shkoly, VGU, Voronezh, 1999, 16

[5] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974

[6] Bulanov A. P., “O skhodimosti kratnoi stepeni, yavlyayuscheisya resheniem nelineinogo differentsialnogo uravneniya”, Algebra i analiz, Materialy konferentsii, posvyaschennoi 100-letiyu B. M. Gagaeva (16–22 iyunya 1997 g., g. Kazan), Izd-vo Kazanskogo matematicheskogo obschestva, Kazan, 1997, 40–41

[7] Kholodniok M., Klich A., Kubichek M., Marek M., Metody analiza nelineinykh dinamicheskikh modelei, Mir, M., 1991