论文标题
亚伯通用系列
Abel universal series
论文作者
论文摘要
给定序列=（r n）n $ \ in $ [0，1）趋向于1，我们考虑了由敞开的单元圆盘d中的Abel Universal系列组成的Abel Universal系列的集合U A（d，），因此，对于单位圆圈中包含的任何紧凑型集k，与t中包含的任何紧凑型集合，不同于t，s set {z $ \ rightarrow $ f（r rightarrow $ f（r n $ \ bullet $ \ bullet $ \ bullet $ \ bullet $ \ bullet $ \ bullet $）| k：n $ \ in $ n}在K上连续功能的空间C（k）中密集。众所周知，u a（d，）在h（d）中是残留的。我们证明，它与任何其他经典的通用全体形态功能都不一致。特别是，它甚至与包含在综合函数的一组方面相提并论，在任何紧凑型集合K $ \ subset $ t中，泰勒在0的泰勒多项式在C（k）中均匀，与T的不同之处。最终，一个亚伯通用系列可以看作是扩张操作员t n：f $ \ rightarrow $ f（r n $ \ bullet $）的通用向量。因此，我们研究（T n）n的动力学特性，例如多宇宙性和（常见）频繁的普遍性。所有证明都是建设性的。
Given a sequence = (r n) n $\in$ [0, 1) tending to 1, we consider the set U A (D,) of Abel universal series consisting of holomorphic functions f in the open unit disc D such that for any compact set K included in the unit circle T, different from T, the set {z $\rightarrow$ f (r n $\bullet$)| K : n $\in$ N} is dense in the space C(K) of continuous functions on K. It is known that the set U A (D,) is residual in H(D). We prove that it does not coincide with any other classical sets of universal holomorphic functions. In particular, it not even comparable in terms of inclusion to the set of holomorphic functions whose Taylor polynomials at 0 are dense in C(K) for any compact set K $\subset$ T different from T. Moreover we prove that the class of Abel universal series is not invariant under the action of the differentiation operator. Finally an Abel universal series can be viewed as a universal vector of the sequence of dilation operators T n : f $\rightarrow$ f (r n $\bullet$) acting on H(D). Thus we study the dynamical properties of (T n) n such as the multi-universality and the (common) frequent universality. All the proofs are constructive.
