Abstract and Applied Analysis

Exponential dichotomy for evolution families on the real line

Adina Luminiţa Sasu

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Abstract

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair ( L p ( , X ) , L q ( , X ) ) . We show that the admissibility of the pair ( L p ( , X ) , L q ( , X ) ) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p q . As applications we obtain characterizations for uniform exponential dichotomy of semigroups.

Article information

Source
Abstr. Appl. Anal., Volume 2006 (2006), Article ID 31641, 16 pages.

Dates
First available in Project Euclid: 30 January 2007

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1170202990

Digital Object Identifier
doi:10.1155/AAA/2006/31641

Mathematical Reviews number (MathSciNet)
MR2217210

Zentralblatt MATH identifier
1137.34343

Citation

Sasu, Adina Luminiţa. Exponential dichotomy for evolution families on the real line. Abstr. Appl. Anal. 2006 (2006), Article ID 31641, 16 pages. doi:10.1155/AAA/2006/31641. https://projecteuclid.org/euclid.aaa/1170202990


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