On some Concepts of (a; b; c)-Trichotomy for Noninvertible Linear Discrete-Time Systems in Banach Spaces

Mărioara Lăpădat; Traian Ceauşu; Raluca Luana Loloa

doi:10.2478/awutm-2014-0016

.blurhash-client-img { display: none !important; }

On some Concepts of (a; b; c)-Trichotomy for Noninvertible Linear Discrete-Time Systems in Banach Spaces

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 52 (2014): Issue 2 (December 2014)

By: Mărioara Lăpădat, Traian Ceauşu and Raluca Luana Loloa

Open Access

|Mar 2015

Abstract

This paper considers three general trichotomy concepts for noninvertible linear discrete-time systems in Banach spaces. Characterizations of these concepts are obtained from the point of view of the projections sequences. Some illustrative examples are given in order to prove that these concepts are distinct.

References

[1] A. I. Alonso, J. Hong, and R. Obaya, Exponential dichotomy and trichotomy for diference equations, Comp. Math. Appl., 38, (1999), 41-4910.1016/S0898-1221(99)00167-4
Search in Google Scholar
[2] M. Babujia, M. Megan, and I. L. Popa, On (h,k)- dichotomy nonautonomous linear difference equations in Banach spaces. International Journal of Differential Equations, (2013), Article ID 76168010.1155/2013/761680
Search in Google Scholar
[3] L. Barreira and C. Vails, Robustness of nonuniform exponential trichotomies in Banach spaces, J. Math. Anal. Appi, 351, (2010), 373-38110.1016/j.jmaa.2008.10.030
Search in Google Scholar
[4] S. Elaydi and O. Hajek, Exponential dichotomy and trichotomy of nonlinear differential equations, Differential Integral Equations, 3, (1990), 1201-122410.1201/9781482293326
Search in Google Scholar
[5] S. Elaydi and K. Janglajew, Dichotomy and trichotomy of difference equations, J. Difference Equ. Appi. 3, (1998), 417-44810.1080/10236199708808113
Search in Google Scholar
[6] M. Lăpădat, Trichotomy for abstract evolution operators, Bui. Stiint. Univ. Politeh. Timis., Series of Mathematical-Physics, 59, (2014)
Search in Google Scholar
[7] L. Biriş and R.L. Lolea, On exponential trichotomy of cocycles in Banach spaces, Analele Univ. Timisoara, to appear
Search in Google Scholar
[8] I. Lopez-Fenner and M. Pinto, (h,k)-trichotomies and asymptotics of nonautonomous differential equations, Computers. Math. Appi, 33, (1997), 105-12410.1016/S0898-1221(97)00080-1
Search in Google Scholar
[9] N. Lupa and M. Megan, Generalized exponential trichotomies for abstract evolution operators on the real line, J. Fund. Space. Appi, (2013), Article ID 40904910.1155/2013/409049
Search in Google Scholar
[10] M. Megan and L. Buliga, Nonuniform exponential trichotomy for difference equations in Banach space, Hot Topics in Operator Theory, Theta Ser. Adv. Math., 9, (2008). 145 - 150
Search in Google Scholar
[11] G. Papaschinopoulos, On exponential trichotomy of linear difference equations, Appi. Anal., 40, (1991), 89 - 10910.1080/00036819108839996
Search in Google Scholar
[12] I. L. Popa, T. Ceausu, and M. Megan, On h-trichotomy of linear discrete-time systems in Banach spaces, Acta Universitatis Apulensis, 39, (2014), 1-1010.17114/j.aua.2014.39.28
Search in Google Scholar
[13] R. S. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential equations, III, J. Differential Equations, 3, (1990), 1201-1224
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/awutm-2014-0016 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

Journal RSS Feed

Language: English

Page range: 145 - 155

Submitted on: Oct 23, 2014

Accepted on: Feb 5, 2015

Published on: Mar 25, 2015

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

Strong (a,

c)-trichotomy,

(a,

c)-trichotomy,

weak (a,

c)-trichotomy linear discrete-time systems

Related subjects:

Mathematics,

General mathematics

© 2015 Mărioara Lăpădat, Traian Ceauşu, Raluca Luana Loloa, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 52 (2014): Issue 2 (December 2014)