拟Hermite-Fejer插值算子的平均收敛准则*
Mean Convergence Criteria for Quasi Hermite-Fejer Interpolating Operator
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摘要:研究了以一类Jacobi正交多项式的零点为插值结点的拟Hermite-Fejer插值算子Q2n+1(w, f,x)的平均收敛性。给出三个判断算子Q2n+1(w,f,x)平均收敛于f(x)的收敛准则。采用循环的证 明方法,证明了它们之间是等价的。Abstract:The mean convergence of quasi Hermite-Fejer interpolation operatorQ2n+1(w, f, x)is studied with the zeros of a kind of Jacobi orthogonal polynomial as interpolation node. Three convergence criteria for discriminating the operatorQ2n+1(w, f, x)converging to f(x)in mean are presented. Their equivalence is proved with cyclic proof.
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Key words:
- orthogonal polynomials/
- interpolation/
- convergence/
- operator
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