Asymptotic Behavior of a Poincaré Recurrence System

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Abstract

We establish asymptotic formulae for the solutions of thefirst order recurrence systemxn+1=(A+Bn)xn,whereAandB n(n=0,1,...) are square matrices and ∑n=0Bn2<∞. As a consequence, we confirma recent conjecture about the asymptotic behavior of the solutionsof the higher order scalar equationu(n+1)=∑ki=0(ci+d i(n))u(n-i).

Original languageEnglish
Pages (from-to)226-243
Number of pages18
JournalJournal of Approximation Theory
Volume91
Issue number2
DOIs
Publication statusPublished - Nov 1 1997

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ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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