Exponential dichotomy of evolution operators in Banach spaces

1992 ◽  
pp. 47-52
Author(s):  
Mihail Megan ◽  
Radu Latcu
Keyword(s):  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Evolution Operators

scholarly journals On uniform exponential splitting for noninvertible evolution operators in Banach Spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 121-131 ◽  
Author(s):  
Claudia Luminiţa Mihiţ ◽  
Codruţa Simona Stoica ◽  
Mihail Megan
Keyword(s):  
Banach Spaces ◽  
Lyapunov Functions ◽  
Exponential Dichotomy ◽  
Evolution Operator ◽  
General Concept ◽  
Integral Inequalities ◽  
Evolution Operators ◽  
Exponential Splitting

Abstract The paper considers the general concept of uniform exponential splitting as a generalization of uniform exponential dichotomy property for evolution operators in Banach spaces. Two characterizations in terms of integral inequalities of Datko-type respectively Lyapunov functions for uniform exponential splitting of a noninvertible evolution operator with respect to invariant projections families are obtained.

scholarly journals On some dichotomy concepts with different growth rates for evolution operators in Banach spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 133-150
Author(s):  
Nicolae Marian Seimeanu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Growth Rates ◽  
Real Numbers ◽  
Evolution Operators

Abstract This paper treats three concepts of (h, k)-dichotomy and their correspondents in the uniform cases. The connections between them are established through examples and counterexamples presented on the Banach space of square-summable sequences of real numbers.

scholarly journals Connections between Some Concepts of Polynomial Trichotomy for Noninvertible Evolution Operators in Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mihai-Gabriel Babuţia ◽  
Nicolae Marian Seimeanu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Evolution Operators

The present paper treats three concepts of nonuniform polynomial trichotomies for noninvertible evolution operators acting on Banach spaces. The connections between these concepts are established through numerous examples and counterexamples for systems defined on the Banach space of square-summable sequences.

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

scholarly journals Datko criteria for uniform instability in Banach spaces

2021 ◽  
Vol 66 (1) ◽  
pp. 115-122
Author(s):  
Rovana Boruga Toma ◽  
Mihail Megan
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Evolution Operators ◽  
Necessary And Sufficient

The main objective of this paper is to present some necessary and sufficient conditions of Datko type for the uniform exponential and uniform polynomial instability concepts for evolution operators in Banach spaces.

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