Abstract
We construct an analog of two-scale relations for basis trigonometric splines with uniform knots corresponding to a linear differential operator of order 2r + 1 with constant coefficients L2r+1(D) = D(D2 + α12 )(D2 + α22 )... (D2 + α r 2 ), where α1, α2,..., α r are arbitrary positive numbers. The properties of nested subspaces of trigonometric splines are analyzed.
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