Bases of trigonometric polynomials formed by shifted Dirichlet kernels / T. P. Lukashenko. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 5. P. 35-40 [Moscow Univ. Math. Bulletin. Vol. 69, N 5, 2014.].
The system of shifts of Dirichlet kernel on (2kπ)/(2n+1), k=0,±1,…,±n, and the system of such shifts of the conjugate Dirichlet kernel with ½ are orthogonal bases in the space of trigonometric polynomials of degree n. The system of shifts of kernels $∑k=mn cos kx and ∑k=mn kx on (2kπ)/(n-m+1), k=0,1,…,n-m, is an orthogonal basis in the space of trigonometric polynomials with the components from m≥1 tо n. There is no orthogonal basis of shifts of any function in this space for 0<m<n.
Key words: orthogonal basis, trigonometric polynomials, Dirichlet kernel, conjugate Dirichlet kernel.