Admissibility for Nonuniform (μ, ν) Contraction and Dichotomy. (23rd December 2012)

• Record Type: Journal Article
• Authors: Jiang, Yongxin; Liao, Fang-fang
• Other Names: Sun Juntao Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-12-23
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/741696
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated ℒ p spaces, with p ∈ ( 1, ∞ ], is admissible for a given evolution process, then this process is a nonuniform ( μ, ν ) contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform ( μ, ν ) contraction and dichotomy is provided.