广义样条及其广义欧拉方程与哈密尔顿特征

GENERALIZED SPLINES AND THEIR GENERALIZED EULER'S EQUATIONS AND HAMILTONIAN CHARACTERISTICS

1.引言和引理 本文的目的是通过研究超约束变分问题引进一类广义样条函数,并借助广义函数Dirac δ来建立其所满足的广义欧拉微分方程和广义哈密尔顿方程,进而刻画这类广义样条函数的特征性质;特别是利用哈密尔顿函数刻画自由结点样条的特征性质. 熟知,最简单的三次样条函数,就有明显的力学意义和变分性质.因此。

Ceneralized splines are defined as the solutions of variational problems with over-requiredconstraints in this paper. By using Dirac δ, the generalized Euler's equations and Hamilton'sequations satisfied by the splines are delivered, and the characteristics of the splines are presen-ted by virtue of Hamiltonian.