Geodesic
Convergence of Fourier sums by polynomials orthogonal on arbitrary lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 60-62

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We study approximation properties of discrete Fourier sums of a function on the segment $[-1,1]$ on an orthonormal system of polynomials representing finite-difference analogs of classical Legendre polynomials. In particular, we find an order of the norm of discrete Fourier sum.
Mots-clés : polynomial
Keywords: orthogonal system, lattice, weight, weight estimate, asymptotic formula, approximation, Fourier sums. 
@article{IVM_2012_7_a7,
     author = {A. A. Nurmagomedov},
     title = {Convergence of {Fourier} sums by polynomials orthogonal on arbitrary lattice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {60--62},
     publisher = {mathdoc},
     number = {7},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_7_a7/}
}
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A. A. Nurmagomedov. Convergence of Fourier sums by polynomials orthogonal on arbitrary lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 60-62. http://geodesic.mathdoc.fr/item/IVM_2012_7_a7/