Geodesic
Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 35-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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The system of shifts of Dirichlet kernel on $\frac{2k\pi}{2n+1}$, $k=0,\pm1,\dots,\pm n$, and the system of such shifts of the conjugate Dirichlet kernel with $\frac12$ are orthogonal bases in the space of trigonometric polynomials of degree $n$. The system of shifts of kernels $\sum_{k=m}^n \cos kx$ and $\sum_{k=m}^n\sin kx$ on $\frac{2k\pi}{n-m+1}$, $k=0,1,\dots,n-m$, is an orthogonal basis in the space of trigonometric polynomials with the components from $m\geqslant1$ tо $n$. There is no orthogonal basis of shifts of any function in this space for $0. 
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     author = {T. P. Lukashenko},
     title = {Bases of trigonometric polynomials consisting of shifts of {Dirichlet} kernels},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a5/}
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T. P. Lukashenko. Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 35-40. http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a5/

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