The Cayley transform of the generator of a polynomially stable $$C_0$$-semigroup

Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F.: Vector-valued Laplace Transforms and Cauchy Problems. Basel: Birkhäuser (2001)

Bátkai, A., Engel, K.J., Prüss, J., Schnaubelt, R.: Polynomial stability of operator semigroups. Math. Nachr. 279, 1425–1440 (2006)

Batty, C.J.K., Chill, R., Tomilov, Y.: Fine scales of decay of operator semigroups. J. Eur. Math. Soc 18, 853–929 (2016)

Batty, C.J.K., Duyckaerts, T.: Non-uniform stability for bounded semi-groups on Banach spaces. J. Evol. Equ. 8, 765–780 (2008)

Batty, C.J.K., Gomilko, A., Tomilov, Y.: A Besov algebra calculus for generators of operator semigroups and related norm-estimates. Math. Ann. 379, 23–93 (2021)

Borichev, A., Tomilov, Y.: Optimal polynomial decay of functions and operator semigroups. Math. Ann. 347, 455–478 (2010)

Cohen, G., Lin, M.: Remarks on rates of convergence of powers of contractions. J. Math. Anal. Appl. 436, 1196–1213 (2016)

Curtain, R.F., Zwart, H.J.: An Introduction to Infinite-Dimensional Linear Systems Theory. New York: Springer (1995)

Eisner, T.: Stability of Operators and Operator Semigroups. Basel: Birkhäuser (2010)

Engel, K.J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. New York: Springer (2000)

Gautschi, W.: Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38, 77–81 (1959)

Gomilko, A.: Cayley transform of the generator of a uniformly bounded $$C_0$$-semigroup of operators. Ukrainian Math. J. 56, 1212–1226 (2004)

Gomilko, A.: Inverses of semigroup generators: a survey and remarks. In: Études opératorielles, Banach Center Publ, pp. 107–142 (2017)

Gomilko, A., Zwart, H.: The Cayley transform of the generator of a bounded $$C_0$$-semigroup. Semigroup Forum 74, 140–148 (2007)

Gomilko, A., Zwart, H., Besseling, N.: Growth of semigroups in discrete and continuous time. Studia Math. 206, 273–292 (2011)

Gomilko, A.M.: Conditions on the generator of a uniformly bounded $$C_0$$-semigroup. Funct. Anal. Appl. 33, 294–296 (1999)

Guo, B.Z., Zwart, H.: On the relation between stability of continuous-and discrete-time evolution equations via the Cayley transform. Integr. equ. oper. theory 54, 349–383 (2006)

Haase, M.: The Functional Calculus for Sectorial Operators. Basel: Birkhäuser (2006)

Haase, M.: Lectures on Functional Calculus. 21st International Internet Seminar, Kiel Univ (2018). Retrieved May 27, 2021, from https://www.math.uni-kiel.de/isem21/en/course/phase1/isem21-lectures-on-functional-calculus

Liu, Z., Rao, B.: Characterization of polynomial decay rate for the solution of linear evolution equation. Angew. Math. Phys. 56, 630–644 (2005)

Nagy, B.S., Foiaş, C.: Harmonic Analysis of Operators on Hilbelt Space. North Holland Publishing Co. (1970)

Ng, A.C.S., Seifert, D.: Optimal rates of decay in the Katznelson-Tzafriri theorem for operators on Hilbert spaces. J. Funct. Anal. 279, Art. no. 108799 (2020)

Paunonen, L.: Perturbation of strongly and polynomially stable Riesz-spectral operators. Systems Control Lett. 60, 234–248 (2011)

Paunonen, L.: Robustness of strongly and polynomially stable semigroups. J. Funct. Anal. 263, 2555–2583 (2012)

Paunonen, L.: Robustness of polynomial stability with respect to unbounded perturbations. Systems Control Lett. 62, 331–337 (2013)

Piskarev, S., Zwart, H.: Crank-Nicolson scheme for abstract linear systems. Numer. Funct. Anal. Optim. 28, 717–736 (2007)

Rastogi, S., Srivastava, S.: Strong and polynomial stability for delay semigroups. J. Evol. Equ. 21, 441–472 (2021)

Rozendaal, J., Seifert, D., Stahn, R.: Optimal rates of decay for operator semigroups on Hilbert spaces. Adv. Math. 346, 359–388 (2019)

Seifert, D.: A quantified Tauberian theorem for sequences. Stud. Math. 227, 183–192 (2015)

Seifert, D.: Rates of decay in the classical Katznelson-Tzafriri theorem. J. Anal. Math. 130, 329–354 (2016)

Shi, D.H., Feng, D.X.: Characteristic conditions of the generation of $$C_0$$ semigroups in a Hilbert space. J. Math. Anal. Appl. 247, 356–376 (2000)

Staffans, O.J.: Well-Posed Linear Systems. Cambridge, UK: Cambridge Univ. Press (2005)

Tomilov, Y.: A resolvent approach to stability of operator semigroups. J. Operator Theory 46, 63–98 (2001)

Weidmann, J.: Linear operators in Hilbert spaces. New York: Springer (1980)