Construction of classes of trigonometric interpolations

About one method of construction of interpolation trigonometric splines

Spline classes in the form of trigonometric interpolation splines are constructed.The method of constructing spline classes in the form of trigonometricfourier series whose coefficients have a certain decreasing order are considered.By grouping members of this series accordingwith the effect of overlaying and introducing a multiplier that provides the interpolation properties of the sum of these series on even grids, we obtain classes of trigonometric interpolation splines.The classes of trigonometric splines include classes of periodic polynomial splines of even and odd power ; at the same time, there exist trigonometric splines that do not have polynomial analogues.