Equivalence of the trigonometric system and its perturbations in Lp(−π,π)
- Autores: Sedletskii A.1
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Afiliações:
- Mechanics and Mathematics Faculty
- Edição: Volume 94, Nº 1 (2016)
- Páginas: 464-467
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224164
- DOI: https://doi.org/10.1134/S1064562416040335
- ID: 224164
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Resumo
Let B be one of the spaces Lp(−π,π), 1 ≤ p < ∞, p ≠ 2, and C[−π,π]. Sufficient conditions under which the “perturbed” trigonometric system \({e^{i{{\left( {n + {\alpha _n}} \right)}^t}}}\), n ∈ Z, is equivalent in B to the trigonometric system eint, n ∈ Z, are found. Under an additional requirement on (αn), a necessary condition is obtained. One of the results is as follows. If (αn) ∈ ls, where 1/s = 1/p - 1/2, then the equivalence specified above takes place, and the exponent s is exact; the space C corresponds to p = ∞. The proofs are based on the application of Fourier multipliers.
Sobre autores
A. Sedletskii
Mechanics and Mathematics Faculty
Autor responsável pela correspondência
Email: sedlet@mail.ru
Rússia, Moscow, 119991