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Some Open Problems Related to Generalized Fourier Series

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Special Functions, Partial Differential Equations, and Harmonic Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 108))

Summary

Let 1 ≤ n 1 < n 2 < ⋯ and let \(\varOmega =\{ -n_{k}\}_{k=1}^{\infty }\cup \{ n_{k}\}_{k=1}^{\infty }\) be an infinite set of natural numbers such that card Ω c = ∞, where \(\varOmega ^{c} =\mathbb{Z}\setminus \varOmega\). We study conditions for which {M(x)e ikx: k ∈ Ω} should be complete and minimal in \(L^{p}(\mathbb{T}),1 \leq p < \infty.\) The problem of describing pairs (Ω, M) for which {M(x)e ikx: k ∈ Ω} is complete and minimal in \(L^{p}(\mathbb{T}),1 \leq p < \infty \) is open.

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Authors and Affiliations

  1. Departamento de Matemáticas, 01.17, Universidad Autónoma de Madrid, Madrid, 28049, Spain

    Kazaros S. Kazarian

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  1. Kazaros S. Kazarian
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Correspondence to Kazaros S. Kazarian .

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Editors and Affiliations

  1. DePaul University, Chicago, Illinois, USA

    Constantine Georgakis

  2. Georgia Southern University, Statesboro, Georgia, USA

    Alexander M. Stokolos

  3. Roosevelt University, Chicago, Illinois, USA

    Wilfredo Urbina

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Kazarian, K.S. (2014). Some Open Problems Related to Generalized Fourier Series. In: Georgakis, C., Stokolos, A., Urbina, W. (eds) Special Functions, Partial Differential Equations, and Harmonic Analysis. Springer Proceedings in Mathematics & Statistics, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-10545-1_10

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