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Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version)

Philippe Dumas 1 
1 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
Abstract : 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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Submitted on : Thursday, August 21, 2008 - 4:19:48 PM
Last modification on : Friday, February 4, 2022 - 3:08:40 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 5:11:50 PM


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  • HAL Id : inria-00294520, version 2
  • ARXIV : 0807.1523



Philippe Dumas. Mean asymptotic behaviour of radix-rational sequences and dilation equations (Extended version). 2008. ⟨inria-00294520v2⟩



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