Geodesic
Sobolev orthogonal systems with two discrete points and Fourier series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 56-66

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We consider properties of systems $\Phi_1$ orthogonal with respect to a discrete-continuous Sobolev inner product of the form $\langle f,g \rangle_S = f(a)g(a)+f(b)g(b)+\int_a^b f'(t)g'(t)dt$. In particular, we study completeness of the $\Phi_1$ systems in the Sobolev space $W^1_{L^2}$. Additionally, we analyze properties of the Fourier series with respect to $\Phi_1$ systems and prove that these series converge uniformly to functions from $W^1_{L^2}$.
Keywords: discrete-continuous inner product, Sobolev inner product, Fabe–Schauder system, Jacobi polynomials with negative parameters, Fourier series, coincidence at the ends of the segment, completeness of Sobolev systems.
Mots-clés : uniform convergence 
@article{IVM_2021_12_a4,
     author = {M. G. Magomed-Kasumov},
     title = {Sobolev orthogonal systems with two discrete points and {Fourier} series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {56--66},
     publisher = {mathdoc},
     number = {12},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_12_a4/}
}
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M. G. Magomed-Kasumov. Sobolev orthogonal systems with two discrete points and Fourier series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 56-66. http://geodesic.mathdoc.fr/item/IVM_2021_12_a4/