论文标题
树木上的普遍谐波功能：普遍性和频繁的普遍性
Generalized Harmonic Functions on Trees: Universality and Frequent Universality
论文作者
论文摘要
最近，已经研究了树$ t $上的谐波函数和经常在树上的通用谐波功能，在field $ \ mathbb {c} $或$ \ mathbb {r} $上占据可分离的fréchet空间$ e $。在本文中，我们允许函数在相当一般的字段$ \ mathbb {f} $上在矢量空间$ e $中获取值。可分离的拓扑矢量空间$ e $的度量是翻译不变的，而不是谐波功能，我们还可以研究由线性组合（$ \ Mathbb {f} $）定义的更通用的功能。与过去的文献不同，我们不认为$ e $是完整的，因此我们提出了一个新的论点，避免了Baire的定理。
Recently, harmonic functions and frequently universal harmonic functions on a tree $T$ have been studied, taking values on a separable Fréchet space $E$ over the field $\mathbb{C}$ or $\mathbb{R}$. In the present paper, we allow the functions to take values in a vector space $E$ over a rather general field $\mathbb{F}$. The metric of the separable topological vector space $E$ is translation invariant and instead of harmonic functions we can also study more general functions defined by linear combinations with coefficients in $\mathbb{F}$. Unlike the past literature, we don't assume that $E$ is complete and therefore we present a new argument, avoiding Baire's theorem.
