Geodesic
On the asymptotics of the basic functions of a generalized Taylor series for some classes of infinitely differentiable functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 56-75.

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The existence of the asymptotics of the basic functions $\varphi_{s,n,k}(x)$ and $\psi_{s,n,p}(x)$ of a generalized Taylor series for nonquasianalytic function class $H_{\rho,2}$ is proved. The first term of the asymptotic expansions of these functions is obtained. 
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V. A. Makarichev. On the asymptotics of the basic functions of a generalized Taylor series for some classes of infinitely differentiable functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 56-75. http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a5/

[1] V. A. Rvachev, “Obobschennye ryady Teilora dlya beskonechno differentsiruemykh funktsii”, Matem. metody analiza dinamicheskikh sistem, 6 (1982), 99–102

[2] V. A. Rvachev, “Finitnye resheniya funktsionalno-differentsialnykh uravnenii i ikh primeneniya”, UMN, 45:1 (271) (1990), 77–103 | MR | Zbl

[3] V. L. Rvachev, V. A. Rvachev, “Ob odnoi finitnoi funktsii”, Dokl. AN USSR, ser. A, 8 (1971), 705–707

[4] V. A. Rvachev, G. A. Starets, “Nekotorye atomarnye funktsii i ikh primenenie”, Dokl. AN USSR, ser. A., 11 (1983), 22–24 | MR | Zbl

[5] V. M. Kuznichenko, “Obobschennye ryady Teilora dlya klassa funktsii $H(\overline\rho,\overline m,r)$”, Matem. zametki, 46:4 (1989), 120–122 | MR | Zbl

[6] Yu. G. Stoyan, V. S. Protsenko, G. P. Manko, Teoriya R-funktsii i aktualnye problemy prikladnoi matematiki, Naukova dumka, K., 1986 | MR

[7] T. V. Rvacheva, “Ob asimptotike bazisnykh funktsii obobschennogo ryada Teilora”, Dokl. NAN Ukrainy, 5 (2003), 37–41

[8] T. V. Rvacheva, “Ob asimptotike bazisnykh funktsii obobschennogo ryada Teilora”, Vestnik Kharkovskogo natsionalnogo un-ta, Seriya “Matematika, prikladnaya matematika i mekhanika”, 602 (2003), 94–104 | Zbl

[9] G. A. Starets, “Skhodimost obobschennykh ryadov Teilora klassov $H_{\rho,m}$”, Matem. metody analiza dinamicheskikh sistem, 9 (1985), 37–39

[10] G. A. Starets, “Postroenie bazisnykh funktsii dlya obobschennykh ryadov Teilora”, Matem. metody analiza dinamicheskikh sistem, 8 (1984), 16–19

[11] E. P. Tomilova, “Primenenie obobschennykh ryadov Teilora dlya resheniya nekotorykh differentsialno-funktsionalnykh uravnenii”, Matem. metody analiza dinamicheskikh sistem, 8 (1984), 33–35

[12] I. I. Malitskii, “Primenenie obobschennykh ryadov Teilora v teorii differentsialno-funktsionalnykh uravnenii s otklonyayuschimsya argumentom”, Dokl. AN USSR, ser. A, 10 (1985), 17–18 | MR

[13] G. A. Starets, Odin klass atomarnykh funktsii i ego primenenie, Diss. ... kand. fiz.-mat. nauk, KhGU, Kharkov, 1985

[14] V. A. Makarichev, “O bazisnykh funktsiyakh obobschennogo ryada Teilora”, Radioelektronnye i kompyuternye sistemy, 3(44) (2010), 27–37 http://www.nbuv.gov.ua/portal/natural/Rks/index.html