  Classes of simple polynomial and simple trigonometric splines given by
Fourier series are considered. It is shown that the class of simple
trigonometric splines includes the class of simple polynomial splines. For some
parameter values, the polynomial splines coincide with the trigonometric ones;
this allows to transfer to such trigonometric splines all the results obtained
for polynomial splines. Thus, it was possible to combine two powerful theories
- the theory of trigonometric Fourier series and the theory of simple
polynomial splines. The above material is illustrated by numerous examples.
