A Method for the Construction of Wavelet Analogs by Means of Trigonometric B-Splines

Аннотация

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 L_2r+1(D) = D(D₂ + α₁² )(D² + α₂² )... (D² + α_r² ), where α₁, α₂,..., α_r are arbitrary positive numbers. The properties of nested subspaces of trigonometric splines are analyzed.