一类奇三角插值多项式算子的收敛性
On the Convergence for a Class of Odd TrigonometricInterpolation Polynomial Operators
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摘要:利用两点修正的方法构造了一类奇三角插值算子,重点证明该算子对以2 π为周期的连续奇函数在全实轴上一致收敛,并且进一步讨论其逼近度Abstract:The paper introduces an odd Trigonometric polynomial operator H n(f:r,x)(where r is a given natural number)based on these values of f(x)(where f(x)∈C 2πand f(x)are even functions)on these nodes(x k=(kπ)/(n+1)) n k=1. H n(f:r,x)uniformly converge to f(x)on the total real axis. The approximation order of H n(f:r,x)reaches the rest approximation order when used to approximate to f(x)wheref(x)∈C 2π,(0 SymbolcB@ j SymbolcB@ r-1)and f(x)is odd function
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