|
Weighted Sobolev orthogonal systems with two discrete points and Fourier series with respect to them
M. G. Magomed-Kasumovab a Daghestan Federal Research Centre of the Russian Academy of Science, 45 M. Gadjiev str., Makhachkala, 367000 Russia
b Southern Mathematical Institute – the Affiliate of Vladikavkaz Scientific Center of Russian Academy of Science, 53 Vatutin str., Vladikavkaz, 362027 Russia
Abstract:
We consider the properties of systems Φ1 orthogonal with respect to a weighted discrete-continuous Sobolev inner product of the form ⟨f,g⟩S=f(a)g(a)+f(b)g(b)+∫baf′(t)g′(t)w(t)dt. The completeness of systems Φ1 in the Sobolev space W1L2w and the relation of Φ1 to systems orthogonal in weighted Lebesgue spaces L2u are studied. We also analyze properties of the Fourier series with respect to systems Φ1. In particular, conditions for the uniform convergence of Fourier series to functions from W1L2 are obtained.
Keywords:
discrete-continuous inner product, Sobolev inner product, Fourier series, uniform convergence, coincidence at the ends of the segment, completeness of Sobolev systems.
Received: 17.12.2023 Revised: 27.02.2024 Accepted: 20.03.2024
Citation:
M. G. Magomed-Kasumov, “Weighted Sobolev orthogonal systems with two discrete points and Fourier series with respect to them”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 11, 35–50
Linking options:
https://www.mathnet.ru/eng/ivm10033 https://www.mathnet.ru/eng/ivm/y2024/i11/p35
|
Statistics & downloads: |
Abstract page: | 58 | Full-text PDF : | 1 | References: | 16 | First page: | 8 |
|