Geodesic
A method for the construction of analogs of wavelets by means of trigonometric $B$-splines
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 320-327

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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.
Keywords: two-scale relation, trigonometric $B$-spline, differential operator, wavelets. 
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     author = {V. T. Shevaldin},
     title = {A method for the construction of analogs of wavelets by means of trigonometric $B$-splines},
     journal = {Trudy Instituta matematiki i mehaniki},
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V. T. Shevaldin. A method for the construction of analogs of wavelets by means of trigonometric $B$-splines. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 320-327. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a29/