Orlicz空间中Müntz有理逼近

The Müntz Rational Approximation in Orlicz Spaces

在多项式逼近、插值逼近、倒数逼近等形式中,有理逼近是函数逼近论的一个重要逼近形式。在工程、信号处理等领域有重要应用。相比多项式虽然有理函数复杂一些,但用有理函数近似表示函数时,能够反映函数的一些属性,而且要比多项式灵活、有效。利用连续模、K-泛函等研究逼近问题的工具,结合不等式技巧在Orlicz空间内讨论了Müntz有理逼近问题,得到了逼近阶的两种估计。

In the problems of polynomial approximation,interpolation approximation and reciprocal approximation,the rational approximation is an important approximation form of function approximation theory.It has important applications in engineering,signal processing.As a kind of nonlinear approximation,the rational approximations attracted much attention.Although the rational function is more complicated than the polynomial,it is more flexible than the polynomial and can reflect some properties of the function.Combined with the tools of modulus of continuous,K-functional and inequality techniques,the two kinds of approximation estimation was obtained.