On the space of periodic ultradifferentiable functions of Roumieu type and its dual
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 89-95
Voir la notice de l'article provenant de la source Math-Net.Ru
With a help of a family ${\mathcal H}$ of convex nondecreasing functions on $[0, \infty)$ we define the space $J({\mathcal H})$ of $2 \pi$-periodic infinitely differentiable functions on the real line with given estimates for all derivatives. It belongs to the class of spaces of ultradifferentiable functions of Roumieu type. A description of the space $G({\mathcal H})$ is obtained in terms of the best trigonometric approximations and the rate of decrease of the Fourier coefficients. A general form of linear continuous functionals on $J({\mathcal H})$ is found. It is shown that some well-known classes of $2 \pi$-periodic functions of Gevrey type are special cases of the spaces $J({\mathcal H})$.
Keywords:
Fourier series, trigonometric polynomials.
Mots-clés : Fourier coefficients
Mots-clés : Fourier coefficients
@article{IVM_2023_4_a7,
author = {I. Kh. Musin},
title = {On the space of periodic ultradifferentiable functions of {Roumieu} type and its dual},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {89--95},
publisher = {mathdoc},
number = {4},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2023_4_a7/}
}
I. Kh. Musin. On the space of periodic ultradifferentiable functions of Roumieu type and its dual. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2023), pp. 89-95. http://geodesic.mathdoc.fr/item/IVM_2023_4_a7/