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Discrete characterizations of h-dichotomy for linear discrete-time systems in Banach spaces Cover

Discrete characterizations of h-dichotomy for linear discrete-time systems in Banach spaces

Open Access
|Jun 2025

References

  1. M. G. Babuţia, M. Megan, Nonuniform exponential dichotomy for discrete dynamical systems in Banach Spaces, Mediterr. J. Math. 13 (2016), 16531667.
  2. R. Boruga (Toma), On uniform dichotomies for the growth rates of linear discrete-time dynamical systems in Banach spaces. In: Olaru, S., Cushing, J., Elaydi, S., Lozi, R. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA2022. Springer Proc. Math. Stat. 444 (2024), 175188.
  3. C. V. Co man, J. J. Schäer, Dichotomies for linear difference equations, Math. Ann. 172 (1967), 139-166.
  4. V. Crai, M. Aldescu, On (h,k)-dichotomy of linear discrete-time systems in Banach spaces. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proc. Math. Stat. 287 (2019), 257-271.
  5. J. Daleckii, M. Krein, Stability of solutions of differential equations in Banach spaces, Translations of Mathematical Monographs Vol. 43, Amer. Math. Soc., Providence, RI, 1974.
  6. R. Datko, Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal. 3 (1972), 428-445.
  7. D. Dragičević, Admissibility and nonuniform polynomial dichotomies, Math. Nachr. 293 (2020), 226-243.
  8. D. Dragičević, A. L. Sasu, B. Sasu, Admissibility and polynomial dichotomy of discrete nonautonomous systems, Carpath. J. Math. 38 (2022), 737-762.
  9. D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer, 1981.
  10. A. GȈainȈa, M. Megan, C. F. Popa, Uniform dichotomy concepts for discrete-time skew evolution cocycles in Banach spaces, Mathematics 9 (2021), 1-11.
  11. Y. Latushkin, T. Radolph, R. Schnaubelt, Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces, J. Dyn. Differ. Equations 10 (1998), 489-510.
  12. T. Li, Die stabilitatsfrage bei differenzengleichungen, Acta Math. 63 (1934), 99-141.
  13. J. L. Massera, J. J. Scha er, Linear differential equations and function spaces, Academic Press, New York, 1966.
  14. M. Megan, C. L. Mihiţ, R. Lolea, On splitting with different growth rates for linear discrete-time systems in Banach spaces, Difference Equations, Discrete Dynamical Systems and Applications, Springer Proc. Math. Stat. 287 (2019), 351-368.
  15. M. Megan, A. L. Sasu, B. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces, Integral Equations Oper. Theory 44 (2002), 71-78.
  16. M. Megan, A. L. Sasu, B. Sasu, Discrete admissibility and exponential dichotomy for evolution families, Discrete Contin. Dyn. Syst. 9 (2003), 383-398.
  17. O. Perron, Die Stabilittsfrage bei Differentialgleichungen, Math. Z. 32 (1930), 703-728.
  18. M. Pinto, Discrete Dichotomies, Comput. Math. Appl. 28 (1994), 259-270.
  19. I.- L. Popa, M. Megan, T. Ceauşu, Exponential dichotomies for linear discrete-time systems in Banach spaces, Appl. Anal. Discrete Math. 6 (2012), 140-155.
  20. P. Preda, M. Megan, On exponential dichotomy of linear discrete-time systems in Banach spaces, An. Univ. Vest Timiş. Ser. Mat.-Inform. 28 (1990), 177-187.
  21. A. L. Sasu, B. Sasu, Discrete admissibility, lpspaces and exponential dichotomy on the real line, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 13 (2006), 551-561.
  22. A. L. Sasu, M. Megan, B. Sasu, On Rolewicz-Zabczyk techniques in the stability theory of dynamical systems, Fixed Point Theory 13 (2012), 205-236.
  23. B. Sasu, A. L. Sasu, Exponential dichotomy and (lp, lq)-admissibility on the half-line, J. Math. Anal. Appl. 316 (2006), 397-408.
  24. B. Sasu, A. L. Sasu, On the dichotomic behavior of discrete dynamical systems on the half-line, Discrete Contin. Dyn. Syst. 33 (2013), 3057-3084.
  25. N. M. Seimeanu, On some concepts of polynomial dichotomy for linear discrete-time systems in Banach spaces, J. Adv. Math. Stud. 8 (2015), 40-52.
  26. N. M. Seimeanu, M. Megan, Three concepts of uniform polynomial dichotomy for discrete-time linear systems in Banach spaces, Proceedings of the International Symposium “Research and Education in Innovation Era”, Section Mathematics, 5th Edition, ”Aurel Vlaicu” University of Arad Publishing House (2014), 77-84.
  27. J. Zabczyk, Remarks on the control of discrete-time distributed parameter systems, SIAM J. Control 12 (1974), 721-735.
DOI: https://doi.org/10.2478/awutm-2025-0004 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 41 - 54
Submitted on: May 28, 2024
Accepted on: Jun 15, 2025
Published on: Jun 25, 2025
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2025 Carmen-Florinela Popa, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.