The work examines norms in of fundamental trigonometric splines of odd and even degrees, which in some cases coincide with polynomial ones. Fundamental trigonometric splines for the case where the con-vergence factors depend on the parameter are also considered. It is shown that an important characteristic of these splines of odd and even degrees is their complete variation. The semi-norms of trigonometric splines of odd degrees are also studied. The given material is illustrated by graphs; so, in particular, an illustration of the property of the least curvature of polynomial splines is given for the first time.

翻译：本文研究了奇次和偶次基本三角样条的范数，这些范数在某些情况下与多项式样条的范数一致。同时，考虑了收敛因子依赖于参数时的基本三角样条。研究表明，奇次和偶次三角样条的一个重要特性是其完全变分。此外，还探讨了奇次三角样条的半范数。文中通过图形对所述内容进行了说明；特别地，首次给出了多项式样条最小曲率性质的图示。