Function theory on the Neil parabola

广义Neil抛物线上的不变度量和不变距离

Invariant metrics and distances on generalized Neil parabolas

给出了广义抛物线上的Carathéodory-Reiffen度量和内Carathéodory距离.事实证明，在这样的抛物线上，Carathéodory距离不是内部的。

Neil代数的Fejér-Rogosinski定理

Fejér-Rogosinski theorem for the Neil algebra

本文证明了Neil代数中函数泰勒展开的部分和在特定半径球上被一致范数有界，且该半径最优。

Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Let $P_{2k}$ be a homogeneous polynomial of degree $2k$ and assume that there exist $C>0$, $D>0$ and $α\ge 0$ such that \begin{equation*} \left\langle P_{2k}f_{m},f_{m}\right\rangle_{L^2(\mathbb{S}^{d-1})}\geq \frac{1}{C\left( m+D\right) ^{α}}\left\langle f_{m},f_{m}\right\rangle_{\mathbb{S}^{d-1}} \end{equation*} for all homogeneous polynomials $f_{m}$ of degree $m.$ Assume that $P_{j}$ for $j=0, \dots ,β<2k$ are homogeneous polynomials of degree $j$. The main result of the paper states that for any entire function $f$ of order $% ρ<\left( 2k-β\right) /α$ there exist entire functions $q$ and …