Properties of Paley–Wiener spaces: sampling sets, contractions, and geometry of the unit ball
Doctoral thesis
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Date
2023-03Metadata
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- PhD theses (TN-IMF) [18]
Original version
Properties of Paley–Wiener spaces: sampling sets, contractions, and geometry of the unit ball by Ilia Zlotnikov, Stavanger : University of Stavanger, 2023 (PhD thesis UiS, no. 689)Abstract
This Thesis is based on five papers, four of which are published and one has been submitted for publication. For convenience of the reader, we also include one chapter that contains a brief overview of the results, some relevant background material, and comments on methods used in the proofs.
The Thesis studies several problems from modern Harmonic analysis. More precisely, we focus on studying various properties of Paley-Wiener spaces: sampling sets, extreme and exposed points of the unit ball, and contraction operators.
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Paper 1: Alexander Rashkovskii, Alexander Ulanovskii, Ilya Zlotnikov, (2023). On 2-dimensional mobile sampling. Applied and Computational Harmonic Analysis 62, 1-23, DOI: 10.1016/j.acha.2022.08.001, preprint: arxiv.org/abs/2005.11193Paper 2: Alexander Ulanovskii, Ilya Zlotnikov, (2021). Reconstruction of bandlimited functions from space-time samples. Journal of Functional Analysis 280 (9), 108962, 1-14, DOI: 10.1016/j.jfa.2021.108962, preprint: arxiv.org/abs/2007.11366
Paper 3: Alexander Ulanovskii, Ilya Zlotnikov, (2022). On geometry of the unit ball of Paley-Wiener space over two symmetric intervals. In press in International Mathematics Research Notices, DOI: 10.1093/imrn/rnac043, preprint: arxiv.org/abs/2108.08093. This paper is not included in Brage due to copyright restrictions.
Paper 4: Aleksei Kulikov, Ilya Zlotnikov, (2022). Contractive projections in Paley-Wiener spaces. In press in Proceedings of the American Mathematical Society, DOI: 10.1090/proc/16336, preprint: https://arxiv.org/abs/2207.09278
Paper 5: Aleksei Kulikov, Alexander Ulanovskii, Ilya Zlotnikov, (2022). Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials. Submitted to journal, preprint: https://arxiv.org/abs/2210.00504
Publisher
University of Stavanger, NorwaySeries
PhD thesis UiS;;689