奇多项式逼近奇函数的失效
Failure of Approximation of Odd Functions by Odd Polynomials
摘要：
构造了单位圆盘上的Hilbert全纯函数空间$H$，使得多项式在$H$中稠密，而奇多项式在$H$中的奇函数中不稠密.因此，在$H$中存在一个函数$f$，它位于其泰勒部分和$s_n(f)$的闭合线性跨度之外，因此它不能通过应用于$s_n(f)$的任何三角求和方法来近似。我们还表明，存在一个功能$f$在$H$，位于其径向扩张$f_r, ~r<1$的封闭的线性跨度之外。
英文摘要：
We construct a Hilbert holomorphic function space $H$ on the unit disk such that the polynomials are dense in $H$, but the odd polynomials are not dense in the odd functions in $H$. As a consequence, there exists a function $f$ in $H$ that lies outside the closed linear span of its Taylor partial sums $s_n(f)$, so it cannot be approximated by any triangular summability method applied to the $s_n(f)$. We also show that there exists a function $f$ in $H$ that lies outside the closed linear span of its radial dilates $f_r, ~r<1$.
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