scholarly journals Pairs of Function Spaces and Exponential Dichotomy on the Real Line

2010 ◽  
Vol 2010 (1) ◽  
pp. 347670 ◽  
Author(s):  
AdinaLuminiţa Sasu
Keyword(s):  
Real Line ◽  
Exponential Dichotomy ◽  
Function Spaces ◽  
The Real

scholarly journals A Remark on Isometries of Absolutely Continuous Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-3
Author(s):  
Alireza Ranjbar-Motlagh
Keyword(s):  
Continuous Function ◽  
Composition Operator ◽  
Real Line ◽  
Weighted Composition Operator ◽  
Function Spaces ◽  
Absolutely Continuous ◽  
The Real ◽  
Absolutely Continuous Function ◽  
Weighted Composition ◽  
Vector Valued

The purpose of this article is to study the isometries between vector-valued absolutely continuous function spaces, over compact subsets of the real line. Indeed, under certain conditions, it is shown that such isometries can be represented as a weighted composition operator.

scholarly journals Exponential dichotomy on the real line: SVD and QR methods

2010 ◽  
Vol 248 (2) ◽  
pp. 287-308 ◽  
Author(s):  
Luca Dieci ◽  
Cinzia Elia ◽  
Erik Van Vleck
Keyword(s):  
Real Line ◽  
Exponential Dichotomy ◽  
The Real ◽  
Qr Methods

scholarly journals Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real Line

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Nicolae Lupa ◽  
Mihail Megan
Keyword(s):  
Differential Equations ◽  
Real Line ◽  
Exponential Dichotomy ◽  
Natural Extension ◽  
Evolution Operators ◽  
The Real ◽  
Exponential Trichotomy ◽  
Whole Space

This paper considers two trichotomy concepts in the context of abstract evolution operators. The first one extends the notion of exponential trichotomy in the sense of Elaydi-Hajek for differential equations to abstract evolution operators, and it is a natural extension of the generalized exponential dichotomy considered in the paper by Jiang (2006). The second concept is dual in a certain sense to the first one. We prove that these types of exponential trichotomy imply the existence of generalized exponential dichotomy on both half-lines. We emphasize that we do not assume the invertibility of the evolution operators on the whole spaceX(unlike the case of evolution operators generated by differential equations).

scholarly journals On function spaces of compact subspaces of Σ-products of the real line

1980 ◽  
Vol 107 (2) ◽  
pp. 135-143 ◽  
Author(s):  
K. Alster ◽  
Roman Pol
Keyword(s):  
Real Line ◽  
Function Spaces ◽  
The Real
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