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

2006 ◽  
Vol 253 (3) ◽  
pp. 515-536 ◽  
Author(s):  
Bogdan Sasu ◽  
Adina Luminiţa Sasu
Keyword(s):  
Real Line ◽  
The Real ◽  
Evolution Families ◽  
Exponential Trichotomy

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 Nonuniform exponential stability for evolution families on the real line

2015 ◽  
Vol 23 (1) ◽  
pp. 199-212
Author(s):  
Claudia Isabela Morariu ◽  
Petre Preda
Keyword(s):  
Exponential Stability ◽  
Real Line ◽  
Exponential Growth ◽  
Sufficient Conditions ◽  
Evolution Family ◽  
Input Output ◽  
The Real ◽  
Perron Method ◽  
Evolution Families ◽  
Nonuniform Exponential Stability

AbstractThe purpose of the present paper is to investigate the problem of nonuniform exponential stability of evolution families on the real line using the input-output technique known in the literature as the Perron method for the study of exponential stability. In this manuscript we describe an evolution family on the real line and we present sufficient conditions for the nonuniform exponential stability of an evolution family on the real line that does not have exponential growth.

scholarly journals Exponential dichotomy for evolution families on the real line

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Adina Luminiţa Sasu
Keyword(s):  
Real Line ◽  
Exponential Dichotomy ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Evolution Family ◽  
The Real ◽  
Evolution Families ◽  
Necessary And Sufficient

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

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real

DERIVATION BASES ON THE REAL LINE (I)

1982 ◽  
Vol 8 (1) ◽  
pp. 67 ◽  
Author(s):  
Thomson
Keyword(s):  
Real Line ◽  
The Real

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

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