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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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