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Exponential trichotomy and p-admissibility for evolution families on the real line

Exponential trichotomy and p-admissibility for evolution families on the real line The aim of this paper is to obtain necessary and sufficient conditions for uniform exponential trichotomy of evolution families on the real line. We prove that if p ∈ (1,∞) and the pair (C b (R,X),C c (R,X)) is uniformly p-admissible for an evolution family [InlineMediaObject not available: see fulltext.] ={U(t,s)} t ≥ s then [InlineMediaObject not available: see fulltext.] is uniformly exponentially trichotomic. After that we analyze when the uniform p-admissibility of the pair (C b (R, X), C c (R, X)) becomes a necessary condition for uniform exponential trichotomy. As applications of these results we study the uniform exponential dichotomy of evolution families. We obtain that in certain conditions, the admissibility of the pair (C b (R,X),L p (R,X)) for an evolution family [InlineMediaObject not available: see fulltext.]={U(t,s)} t ≥ s is equivalent with its uniform exponential dichotomy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Exponential trichotomy and p-admissibility for evolution families on the real line

Mathematische Zeitschrift , Volume 253 (3) – Jan 26, 2006

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-005-0920-8
Publisher site
See Article on Publisher Site

Abstract

The aim of this paper is to obtain necessary and sufficient conditions for uniform exponential trichotomy of evolution families on the real line. We prove that if p ∈ (1,∞) and the pair (C b (R,X),C c (R,X)) is uniformly p-admissible for an evolution family [InlineMediaObject not available: see fulltext.] ={U(t,s)} t ≥ s then [InlineMediaObject not available: see fulltext.] is uniformly exponentially trichotomic. After that we analyze when the uniform p-admissibility of the pair (C b (R, X), C c (R, X)) becomes a necessary condition for uniform exponential trichotomy. As applications of these results we study the uniform exponential dichotomy of evolution families. We obtain that in certain conditions, the admissibility of the pair (C b (R,X),L p (R,X)) for an evolution family [InlineMediaObject not available: see fulltext.]={U(t,s)} t ≥ s is equivalent with its uniform exponential dichotomy.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jan 26, 2006

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