【作者】 文晓霞；

【导师】 侯象乾；

【作者基本信息】 宁夏大学 ， 基础数学， 2004， 硕士

【摘要】 本文对前人的关于三角插值的一些结果做进一步的研究，主要包含以下两个方面的内容： 1．研究了双周期（0，δ^M）三角插值问题，给出插值基多项式；该插值问题的解决大大降低了对被插值函数可微性的要求，并且得到逼近结果； 2．讨论以π为周期的反周期函数的（0，δ^m），（0，δ^p）插值问题，（0，m₁，m₂，m₃）插值问题及部分双周期情形解的存在性，其中也包含了许多反周期函数的基本问题的讨论。更多还原

【Abstract】 Some- former results on trigonometric interpolation were studied deeply in this paper which contains 2 aspects as following:1. The 2-periodic (o,δM)- trigonometric interpolation problem was studied, and then some fundamental polynomials of interpolation were established; Differentiability of the interpolated function was dropped really through solving the problem and some approximation results were obtained.2. Solvability of (0,δm),(o,δp)(o,m1],Am2,/m3)-interpolation problems on π -antiperiodic function and some of 2-oeriodic situation were discussed, and some fundamental problems on ;π-antiperiodic function were considered in this aspect.更多还原