Exponential dichotomy on the real line: SVD and QR methods

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).

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Exponential Dichotomy on the Real Line and Admissibility of Function Spaces

Integral Equations and Operator Theory ◽

10.1007/s00020-004-1347-z ◽

2005 ◽

Vol 54 (1) ◽

pp. 113-130 ◽

Cited By ~ 21

Author(s):

Adina Luminiţa Sasu ◽

Bogdan Sasu

Keyword(s):

Real Line ◽

Exponential Dichotomy ◽

Function Spaces ◽

The Real ◽

Admissibility Of Function Spaces

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Pairs of Function Spaces and Exponential Dichotomy on the Real Line

Advances in Difference Equations ◽

10.1186/1687-1847-2010-347670 ◽

2010 ◽

Vol 2010 (1) ◽

pp. 347670 ◽

Cited By ~ 3

Author(s):

AdinaLuminiţa Sasu

Keyword(s):

Real Line ◽

Exponential Dichotomy ◽

Function Spaces ◽

The Real

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Nonuniform Exponential Dichotomy for Evolution Families on the Real Line

Mediterranean Journal of Mathematics ◽

10.1007/s00009-014-0484-0 ◽

2014 ◽

Vol 13 (1) ◽

pp. 171-189 ◽

Cited By ~ 2

Author(s):

Petre Preda ◽

Claudia Morariu

Keyword(s):

Real Line ◽

Exponential Dichotomy ◽

The Real ◽

Evolution Families ◽

Nonuniform Exponential Dichotomy

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Detecting exponential dichotomy on the real line: SVD and QR algorithms

BIT Numerical Mathematics ◽

10.1007/s10543-010-0306-0 ◽

2011 ◽

Vol 51 (3) ◽

pp. 555-579 ◽

Cited By ~ 14

Author(s):

Luca Dieci ◽

Cinzia Elia ◽

Erik Van Vleck

Keyword(s):

Real Line ◽

Exponential Dichotomy ◽

The Real

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Exponential dichotomy for evolution families on the real line

Abstract and Applied Analysis ◽

10.1155/aaa/2006/31641 ◽

2006 ◽

Vol 2006 ◽

pp. 1-16 ◽

Cited By ~ 7

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.

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The properties of Bessel-type fractional derivatives and integrals

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i8.203 ◽

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.

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