Email this article A Sobolev Orthogonal System of Functions Generated by a Walsh System
- Authors: Magomed-Kasumov M.G.1,2
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Affiliations:
- Vladikavkaz Scientific Center of Russian Academy of Sciences
- Daghestan Scientific Center of Russian Academy of Sciences
- Issue: Vol 105, No 3-4 (2019)
- Pages: 543-549
- Section: Article
- URL: https://journal-vniispk.ru/0001-4346/article/view/151666
- DOI: https://doi.org/10.1134/S0001434619030271
- ID: 151666
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Abstract
Properties of functions from the Sobolev orthogonal system \(\mathfrak{W}_{r}\) generated by the Walsh system are studied. In particular, recurrence relations for functions from \(\mathfrak{W}_{1}\) are obtained. The uniform convergence of Fourier series in the system \(\mathfrak{W}_{r}\) to functions f from the S obolev spaces \(W_{{L^p}}^r\), p ≥ 1, r = 1, 2,… is proved.
About the authors
M. G. Magomed-Kasumov
Vladikavkaz Scientific Center of Russian Academy of Sciences; Daghestan Scientific Center of Russian Academy of Sciences
Author for correspondence.
Email: rasuldev@gmail.com
Russian Federation, Vladikavkaz, 362008; Makhachkala, 367025
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