A method for the construction of analogs of wavelets by means of trigonometric $B$-splines

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 $ {\mathcal L}_{2r+1}(D)=D(D^2+\alpha_1^2)(D^2+\alpha_2^2)\ldots (D^2+\alpha_r^2), $ where $\alpha_1,\alpha_2,\ldots,\alpha_r$ are arbitrary positive numbers. The properties of embedded subspaces of trigonometric splines are analyzed.