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Completeness and basis properties of systems of exponentials in weighted spaces L p(−π, π)

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Abstract

We consider the system of exponentials \(e(\Lambda ) = \{ e^{i\lambda _n t} \} _{n \in \mathbb{Z}} \), where

$$\lambda _n = n + \left( {\frac{{1 + \alpha }}{p} + l(\left| n \right|)} \right) sign n,$$

l(t) is a slowly varying function, and l(t) → 0, t → ∞. We obtain an estimate for the generating function of the sequence {λn} and, with its help, find a completeness criterion and a basis condition for the system e(Λ) in the weight spaces L p(−π, π). We also study some special cases of the function l(t).

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Authors and Affiliations

  1. Moscow State University, Russia

    A. A. Yukhimenko

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  1. A. A. Yukhimenko
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Original Russian Text © A. A. Yukhimenko, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 5, pp. 776–788.

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Yukhimenko, A.A. Completeness and basis properties of systems of exponentials in weighted spaces L p(−π, π). Math Notes 81, 695–707 (2007). https://doi.org/10.1134/S0001434607050161

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  • DOI: https://doi.org/10.1134/S0001434607050161

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