Geodesic
Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 57-61.

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

By a given family of convex functions on the real axis that grow at infinity faster than any linear function and by a certain logarithmically convex sequence of positive numbers, we construct the space of infinitely differentiable functions on the real line. Under the condition of a logarithmic gap between weight functions, we prove the possibility of approximation by polynomials in this space.
Mots-clés : Fourier–Laplace transform
Keywords: entire function, convex function, Young–Fenchel transform. 
@article{INTO_2019_162_a5,
     author = {I. Kh. Musin},
     title = {Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {57--61},
     publisher = {mathdoc},
     volume = {162},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_162_a5/}
}
TY  - JOUR
AU  - I. Kh. Musin
TI  - Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 57
EP  - 61
VL  - 162
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_162_a5/
LA  - ru
ID  - INTO_2019_162_a5
ER  - 
%0 Journal Article
%A I. Kh. Musin
%T Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 57-61
%V 162
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_162_a5/
%G ru
%F INTO_2019_162_a5
I. Kh. Musin. Approximation of infinitely differentiable functions on the real line by polynomials in weighted spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 57-61. http://geodesic.mathdoc.fr/item/INTO_2019_162_a5/

[1] Zharinov V. V., “Kompaktnye semeistva LVP i prostranstva $FS$ i $DFS$”, Usp. mat. nauk., 34:4 (1979), 97–131 | MR | Zbl

[2] Mandelbroit S., Primykayuschie ryady, regulyarizatsiya posledovatelnostei, primeneniya, IL, M., 1955

[3] Musin I. Kh., “O preobrazovanii Fure—Laplasa funktsionalov na vesovom prostranstve beskonechno differentsiruemykh funktsii”, Mat. sb., 191:10 (2000), 57–86 | DOI | Zbl

[4] Musin I. Kh., Vesovye prostranstva beskonechno differentsirumykh funktsii, Diss. na soisk. uch. step. d.f.-m.n., IMVTs UNTs RAN, Ufa, 2004

[5] Musin I. Kh., Popenov S. V., “O vesovom prostranstve beskonechno differentsiruemykh funktsii v $\mathbb{R}^n$”, Ufim. mat. zh., 2:3 (2010), 52–60

[6] Sebashtyan-i-Silva Zh., “O nekotorykh klassakh lokalno vypuklykh prostranstv, vazhnykh v prilozheniyakh”, Matematika., 1:1 (1957), 60–77

[7] Taylor B. A., “Analytically uniform spaces of infinitely differentiable functions”, Commun. Pure Appl. Math., 24:1 (1971), 39–51 | DOI | MR | Zbl