On Representation of a Solution to the Cauchy Problem by a Fourier Series in Sobolev-Orthogonal Polynomials Generated by Laguerre Polynomials

Шарапудинов, И. И.; Magomed-Kasumov, M. G.

doi:10.1134/s0012266118010068

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R M Gadzhimirzaev1

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2018

2024

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Cited by 8 publications

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“….) is used as the generating system, were considered in the works [5][6][7][8][9][10]. In particular, in the paper [5] the following theorem was proved.…”

Section: R M Gadzhimirzaevmentioning

confidence: 99%

Sobolev-Orthonormal System of Functions Generated by the System of Laguerre Functions

Gadzhimirzaev¹

2019

Issues of Analysis

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We consider the system of functions λ α r,n (x) (r ∈ N, n = 0, 1, 2,. . .), orthonormal with respect to the Sobolev-type inner product f, g = r−1 ν=0 f (ν) (0)g (ν) (0)+ ∞ 0 f (r) (x)g (r) (x)dx and generated by the orthonormal Laguerre functions. The Fourier series in the system {λ α r,n (x)} ∞ k=0 is shown to uniformly converge to the function f ∈ W r L p for 4 3 < p < 4, α 0, x ∈ [0, A], 0 A < ∞. Recurrence relations are obtained for the system of functions λ α r,n (x). Moreover, we study the asymptotic properties of the functions λ α 1,n (x) as n → ∞ for 0 x ω, where ω is a fixed positive real number.

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“….) is used as the generating system, were considered in the works [5][6][7][8][9][10]. In particular, in the paper [5] the following theorem was proved.…”

Section: R M Gadzhimirzaevmentioning

confidence: 99%