M. G. Magomed-Kasumov, “The uniform convergence of Fourier series in a system of the Sobolev orthogonal polynomials associated to ultraspherical Jacobi polynomials”, Sibirsk. Mat. Zh., 2024, Volume 65, Number 6,Pages <nobr>1173

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The uniform convergence of Fourier series in a system of the Sobolev orthogonal polynomials associated to ultraspherical Jacobi polynomials

M. G. Magomed-Kasumov^ab

^a Daghestan Federal Research Center, Makhachkala, Russia
^b Vladikavkaz Scientific Center, Vladikavkaz, Russia

Abstract: We obtain some necessary and sufficient conditions on a parameter $\alpha$ that ensure that Fourier series in the Sobolev system of polynomials associated to the ultraspherical Jacobi polynomials converge uniformly on $[-1,1]$ to functions in the Sobolev space $W^r_{L^1_{\rho(\alpha)}}$, where $\rho(\alpha)$ is the ultraspherical weight.

Keywords: Sobolev inner product, Jacobi polynomials, Fourier series, uniform convergence, Sobolev space, ultraspherical weight.

UDC: 517.5

MSC: 35R30

Received: 13.07.2024
Revised: 18.09.2024
Accepted: 23.10.2024

DOI: 10.33048/smzh.2024.65.609