最佳有理L_p逼近的特征与性质

The characteristic of the best rational L_p-approximation

在函数逼近中 ,用有理函数作为逼近工具要比多项式优越得多 ,特别对一些含有奇点的函数更是如此。而有理逼近的特征与性质是有理逼近研究的主要问题之一。利用 Lebesgue积分的性质证明最佳有理逼近的特征定理 ,并由该定理证明非有理函数的最佳逼近元必是正规的 ,其误差函数至少有 m +n

The rational function is superior to the polynomial in approximation theory, especially to the function with pole. The characteristic of rational approximation is one of the essential problem for approximation theory. The characteristic theorem of the best rational L p approximation by Lebesgue integral is proved. By means of the theorem, it is proved that the best element of an approximation of non rational function is normal and the sign of error function changes at least m+n+1 times.