中文摘要：

近年来三角样条的相关理论发展迅速,取得了丰硕的成果,但仍然存在一些问题,尤其是在均匀结点的三阶三角样条的结构并不清晰。针对此问题,首先给出了均匀结点条件下的三阶三角样条函数的定义,这种三阶三角样条函数具有7个自由参数,因而自由度更大。为了分析其结构,通过讨论相邻2段三角函数的二阶光滑性限制条件,给出了关于这类样条函数构造的结构定理,该定理表明相邻一段三角样条函数表达式可以表达为前一段三角样条函数表达式与特定的带参数的三阶样条函数之和,这为构造具体三阶三角样条带来了方便。还给出了有限多结点条件下此类样条函数空间的维数定理。最后,通过结构定理给出了几个相关的例子。

英文摘要：

In recent years,the theory of trigonometric splines develops dramatically,and fruitful achievements have been made.However,some little information has been done on the structures of trigonometric splines.To solve this problem,we first propose the definition of cubic uniform trigonometric spline functions.This kind of splines has seven parameters in each interval which provide flexibilities in practical applications.To investigate the structures of proposed splines,we consider the second order continuity limitation imposed on two adjacent segments of trigonometric function,then we derive the structure theorem.This theorem demonstrates that the spline expression in each interval can be expressed as the sum of the previous cubic trigonometric function and one specific trigonometric function,which provide a more convenient approach in the design of trigonometric splines.Furthermore,we propose a dimension theorem of this kind of spline function with finite nodes.Finally,we give several related examples according to the structure theorem.