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

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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. 
@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/}
}
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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/