变阶可解族的带权逼近与插值逼近(英文)

On Weighted and Interpolatory Varisolvent Chebyshev Approximation

中文摘要:

      本文讨论了变阶可解逼近族的插值逼近和带权逼近(权在插值点集Z上趋于无穷而在Z外为1)的关系.指出对变阶可解族而言,当逼近解为非亏损时,稠密性假设是自然满足的,且此时的最佳插值逼近等于该带权最佳逼近的极限.

英文摘要:

      In this paper, we concluded that the Density hypothesis in [5,6,8] is naturally satisfied for varisolvent family; if the best interpolatory Chebyshev approximation on an interval [a,b] is nondegenerate, then there are close relations between the best interpola-tory Chebyshev approximation on [a, b] and the best weighted Chebyshev approximation on subsets of [a, b].