Geodesic
Basis property of the Legendre polynomials in variable exponent Lebesgue spaces
Sbornik. Mathematics, Tome 215 (2024) no. 2, pp. 234-249 Cet article a éte moissonné depuis la source Math-Net.Ru

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Sharapudinov proved that the Legendre polynomials form a basis of the Lebesgue space with variable exponent $p(x)$ if $p(x) > 1$ satisfies the Dini–Lipschitz condition and is constant near the endpoints of the orthogonality interval. We prove that the system of Legendre polynomials forms a basis of these spaces without the condition that the variable exponent be constant near the endpoints. Bibliography: 9 titles.
Keywords: variable exponent, basis, the Dini–Lipschitz condition.
Mots-clés : Lebesgue space, Legendre polynomials 
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M. G. Magomed-Kasumov; T. N. Shakh-Emirov; R. M. Gadzhimirzaev. Basis property of the Legendre polynomials in variable exponent Lebesgue spaces. Sbornik. Mathematics, Tome 215 (2024) no. 2, pp. 234-249. http://geodesic.mathdoc.fr/item/SM_2024_215_2_a5/

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