The space of entire sequences (Q2725625)

Extract from the paper: A complex sequence \(x= \{x_k\}\) is called an entire sequence if \(|x_k|^{1/k}\to 0\) as \(k\to\infty\). The set of all entire sequences will be denoted by \(\Gamma\). A complex sequence \(x= \{x_k\}\) is called an analytic sequence if \(\{|x_k|^{1/k}\}\) is bounded. The set of analytic sequences is denoted by \(\Lambda\). This paper is partly a survey of known results and partly a gist of new results on \(\Gamma\).NEWLINENEWLINEFor the entire collection see [Zbl 0960.00019].