论文标题
奇数多项式近似奇数函数的近似失败
Failure of Approximation of Odd Functions by Odd Polynomials
论文作者
论文摘要
我们在设备磁盘上构建了Hilbert Holomorthic函数$ H $ $ H $，以使多项式在$ H $中密集，但是奇数多项式在$ H $中的奇数函数中并不密集。结果，存在一个函数$ f $ in $ h $中的$ f $，该函数位于其taylor partial sugs $ s_n（f）$之外，因此无法通过应用于$ s_n（f）$的任何三角形总和方法来近似。我们还表明，存在$ h $中的功能$ f $，其径向封闭的线性跨度扩大了$ f_r，〜r <1 $。
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 $f_r, ~r<1$.
