Open Access
Volume 29, 2023
Article Number 45
Number of page(s) 42
Published online 12 June 2023
  1. W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups. Trans. Amer. Math. Soc. 309 (1988) 837–852. [CrossRef] [MathSciNet] [Google Scholar]
  2. W. Arendt, C.J.K. Batty, M. Hieber and F. Neubrander, Vector-valued Laplace Transforms and Cauchy Problems. Birkhäuser, Basel (2001). [CrossRef] [Google Scholar]
  3. A. Bátkai, K.-J. Engel, J. Prüss and R. Schnaubelt, Polynomial stability of operator semigroups. Math. Nachr. 279 (2006) 1425–1440. [CrossRef] [MathSciNet] [Google Scholar]
  4. C.J.K. Batty and T. Duyckaerts, Non-uniform stability for bounded semi-groups on Banach spaces. J. Evol. Equ. 8 (2008) 765–780. [CrossRef] [MathSciNet] [Google Scholar]
  5. C.J.K. Batty and D. Seifert, Some developments around the Katznelson-Tzafriri theorem. Acta Sci. Math. (Szeged) 88 (2022) 53–84. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Borichev and Yu. Tomilov, Optimal polynomial decay of functions and operator semigroups. Math. Ann. 347 (2010) 455–478. [CrossRef] [MathSciNet] [Google Scholar]
  7. R. Chill, D. Seifert and Yu. Tomilov. Semi-uniform stability of operator semigroups and energy decay of damped waves. Philos. Trans. Roy. Soc. A 378 (2020) 20190614. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  8. G. Cohen and M. Lin, Remarks on rates of convergence of powers of contractions. J. Math. Anal. Appl. 436 (2016) 1196–1213. [CrossRef] [MathSciNet] [Google Scholar]
  9. R.F. Curtain and H.J. Zwart, An Introduction to Infinite-Dimensional Systems: A State Space Approach. Springer, New York (2020). [Google Scholar]
  10. T. Eisner, Stability of Operators and Operator Semigroups. Birkhäuser, Basel (2010). [CrossRef] [Google Scholar]
  11. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations. Springer, New York (2000). [Google Scholar]
  12. I. Gohberg, S. Goldberg and M.A. Kaashoek, Classes of Linear Operators, Vol. I. Birkhäuser, Basel (1990). [CrossRef] [Google Scholar]
  13. A.M. Gomilko, Conditions on the generator of a uniformly bounded C0-semigroup. Funct. Anal. Appl. 33 (1999) 294–296. [CrossRef] [MathSciNet] [Google Scholar]
  14. B.-Z. Guo and J.-M. Wang, Control of Wave and Beam PDEs: The Riesz Basis Approach. Springer, Cham (2019). [CrossRef] [Google Scholar]
  15. M. Haase, The Functional Calculus for Sectorial Operators. Birkhäuser, Basel (2006). [Google Scholar]
  16. R.M. Hain, Classical polylogarithms, in Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., Vol. 55, part 2, (1994) 3–42. [CrossRef] [Google Scholar]
  17. Z. Liu and B. Rao, Characterization of polynomial decay rate for the solution of linear evolution equation. Angew. Math. Phys. 56 (2005) 630–644. [CrossRef] [MathSciNet] [Google Scholar]
  18. H. Logemann, R. Rebarber and S. Townley, Stability of infinite-dimensional sampled-data systems. Trans. Amer. Math. Soc. 355 (2003) 3301–3328. [CrossRef] [MathSciNet] [Google Scholar]
  19. Y.I. Lyubich and V.Q. Phông, Asymptotic stability of linear differential equations in Banach spaces. Studia Math. 88 (1988) 37–42. [CrossRef] [MathSciNet] [Google Scholar]
  20. A.C.S. Ng and D. Seifert, Optimal rates of decay in the Katznelson-Tzafriri theorem for operators on Hilbert spaces. J. Funct. Anal. 279 (2020) Art. no. 108799. [Google Scholar]
  21. L. Pandolfi and H. Zwart, Stability of perturbed linear distributed parameter systems. Syst. Control Lett. 17 (1991) 257–264. [Google Scholar]
  22. L. Paunonen, Perturbation of strongly and polynomially stable Riesz-spectral operators. Syst. Control Lett. 60 (2011) 234–248. [Google Scholar]
  23. L. Paunonen, Robustness of strongly and polynomially stable semigroups. J. Funct. Anal. 263 (2012) 2555–2583. [CrossRef] [MathSciNet] [Google Scholar]
  24. L. Paunonen, Robustness of polynomial stability with respect to unbounded perturbations. Syst. Control Lett. 62 (2013) 331–337. [Google Scholar]
  25. L. Paunonen, Polynomial stability of semigroups generated by operator matrices. J. Evol. Equ. 14 (2014) 885–911. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Paunonen, Robustness of strong stability of semigroups. J. Diff. Equ. 257 (2014) 4403–4436. [CrossRef] [Google Scholar]
  27. L. Paunonen, On robustness of strongly stable semigroups with spectrum on iℝ, in Semigroups of Operators -Theory and Applications. Springer, Cham (2015) 105–121. [CrossRef] [Google Scholar]
  28. A.J. Pritchard and S. Townley, Robustness of linear systems. J. Diff. Equ. 77 (1989) 254–286. [CrossRef] [Google Scholar]
  29. S. Rastogi and S. Srivastava, Strong and polynomial stability for delay semigroups. J. Evol. Equ. 21 (2021) 441–472. [CrossRef] [MathSciNet] [Google Scholar]
  30. R. Rebarber and S. Townley, Nonrobustness of closed-loop stability for infinite-dimensional systems under sample and hold. IEEE Trans. Automat. Control 47 (2002) 1381–1385. [CrossRef] [MathSciNet] [Google Scholar]
  31. R. Rebarber and S. Townley, Robustness with respect to sampling for stabilization of Riesz spectral systems. IEEE Trans. Automat. Control 51 (2006) 1519–1522. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Rozendaal, D. Seifert and R. Stahn, Optimal rates of decay for operator semigroups on Hilbert spaces. Adv. Math. 346 (2019) 359–388. [CrossRef] [MathSciNet] [Google Scholar]
  33. D. Seifert, A quantified Tauberian theorem for sequences. Stud. Math. 227 (2015) 183–192. [CrossRef] [Google Scholar]
  34. D. Seifert, Rates of decay in the classical Katznelson-Tzafriri theorem. J. Anal. Math. 130 (2016) 329–354. [CrossRef] [MathSciNet] [Google Scholar]
  35. D.-H. Shi and D.-X. Feng, Characteristic conditions of the generation of C0 semigroups in a Hilbert space. J. Math. Anal. Appl. 247 (2000) 356–376. [CrossRef] [MathSciNet] [Google Scholar]
  36. Yu. Tomilov, A resolvent approach to stability of operator semigroups. J. Operator Theory 46 (2001) 63–98. [MathSciNet] [Google Scholar]
  37. M. Tucsnak and G. Weiss, Observation and Control of Operator Semigroups. Birkhäuser, Basel (2009). [CrossRef] [Google Scholar]
  38. M. Wakaiki, Strong stability of sampled-data Riesz-spectral systems. SIAM J. Control Optim. 59 (2021) 3498–3523. [CrossRef] [MathSciNet] [Google Scholar]
  39. M. Wakaiki, The Cayley transform of the generator of a polynomially stable C0-semigroup. J. Evol. Equ. 21 (2021) 4575–4597. [CrossRef] [MathSciNet] [Google Scholar]
  40. C.-Z. Xu and G. Sallet, On spectrum and Riesz basis assignment of infinite-dimensional linear systems by bounded linear feedbacks. SIAM J. Control Optim. 34 (1996) 521–541. [CrossRef] [MathSciNet] [Google Scholar]

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