Bases of trigonometric polynomials consisting of shifts of Dirichlet kernelsстатья
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Аннотация:The system of shifts of Dirichlet kernel on 2kπ2n+1, k = 0, ± 1, …, ± n, and the system of such shifts of conjugate Dirichlet kernels with 12 are orthogonal bases in the space of trigonometric polynomials of degree n. The system of shifts of the kernels Σnk=m cos kx and Σnk=m sin kx on 2kπn−m+1, k = 0, 1, …, n−m, is an orthogonal basis in the space of trigonometric polynomials with the components from m ⩾ 1 to n. There is no orthogonal basis of shifts of any function in this space for 0 < m < n.