根有理序列和膨胀方程的平均渐近性（扩展版）
Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version)
摘要：
从形式语言理论出发，通过固定基数记数系统，基有理序列的生成级数是有理形式幂级数。对于每个具有复值的根有理序列，我们提供了其Cesàro均值序列的渐近展开。渐近展开的精度取决于序列的线性表示的联合谱半径;系数通过一些膨胀方程获得。证明是基于初等线性代数。
英文摘要：
The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence; the coefficients are obtained through some dilation equations. The proofs are based on elementary linear algebra.
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