Asymptotic behaviour of semigroups of operators

 Access to full text

 Full (PDF)

1. [1] H. Alexander, On a problem of Stolzenberg in polynomial convexity, Illinois J. Math. 22 (1978), 149-160. Zbl0376.32013
2. [2] G. R. Allan, A. G. O'Farrell and T. J. Ransford, A Tauberian theorem arising in operator theory, Bull. London Math. Soc. 19 (1987), 537-545. Zbl0652.46041
3. [3] G. R. Allan and T. J. Ransford, Power-dominated elements in a Banach algebra, Studia Math. 94 (1989), 63-79. Zbl0705.46021
4. [4] W. Arendt, Resolvent positive operators, Proc. London Math. Soc. 54 (1987), 321-349. Zbl0617.47029
5. [5] W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852. Zbl0652.47022
6. [6] W. Arendt and C. J. K. Batty, A complex Tauberian theorem and mean ergodic semigroups, preprint. Zbl0836.47032
7. [7] W. Arendt, F. Neubrander and U. Schlotterbeck, Interpolation of semigroups and integrated semigroups, Semesterbericht Funktionalanalysis Tübingen 15 (1988/89), 1-14. Zbl0782.47035
8. [8] W. Arendt and J. Prüss, Vector-valued Tauberian theorems and asymptotic behavior of linear Volterra equations, SIAM J. Appl. Math. 23 (1992), 412-448. Zbl0765.45009
9. [9] R. Arens, Inverse-producing extensions of normed algebras, Trans. Amer. Math. Soc. 88 (1958), 536-548. Zbl0082.11105
10. [10] C. J. K. Batty, Tauberian theorems for the Laplace-Stieltjes transform, ibid. 322 (1990), 783-804. Zbl0716.44001
11. [11] C. J. K. Batty and D. A. Greenfield, On the invertibility of isometric semigroup representations, preprint. Zbl0803.47033
12. [12] C. J. K. Batty and Vũ Quôc Phóng, Stability of individual elements under one-parameter semigroups, Trans. Amer. Math. Soc. 322 (1990), 805-818. 
13. [13] C. J. K. Batty and Vũ Quôc Phóng, Stability of strongly continuous representations of abelian semigroups, Math. Z. 209 (1992), 75-88. 
14. [14] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. Zbl0457.47030
15. [15] O. El Mennaoui, Comportement asymptotique des semi-groupes intégrés, J. Comput. Appl. Math., to appear. 
16. [16] J. Esterle, E. Strouse and F. Zouakia, Theorems of Katznelson-Tzafriri type for contractions, J. Funct. Anal. 94 (1990), 273-287. Zbl0723.47013
17. [17] J. Esterle, E. Strouse and F. Zouakia, Stabilité asymptotique de certains semigroupes d'opérateurs, J. Operator Theory, to appear. 
18. [18] I. Gelfand, Zur Theorie der Charaktere der abelschen topologischen Gruppen, Mat. Sb. 9 (51) (1941), 49-50. Zbl67.0407.02
19. [19] D. A. Greenfield, D.Phil. thesis, Oxford, in preparation. 
20. [20] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc., Providence, 1957. 
21. [21] S. Huang and F. Räbiger, Superstable $C_0$-semigroups on Banach spaces, preprint. Zbl0798.47034
22. [22] A. E. Ingham, On Wiener's method in Tauberian theorems, Proc. London Math. Soc. 38 (1935), 458-480. Zbl0010.35202
23. [23] Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), 313-328. Zbl0611.47005
24. [24] J. Korevaar, On Newman's quick way to the prime number theorem, Math. Intelligencer 4 (1982), 108-115. Zbl0496.10027
25. [25] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985. 
26. [26] Yu. I. Lyubich, On the spectrum of a representation of an abelian topological group, Dokl. Akad. Nauk SSSR 200 (1971), 777-780 (in Russian); English transl.: Soviet Math. Dokl. 12 (1971), 1482-1486. 
27. [27] Yu. I. Lyubich, Introduction to the Theory of Banach Representations of Groups, Birkhäuser, Basel, 1988. 
28. [28] Yu. I. Lyubich and Vũ Quôc Phóng, Asymptotic stability of linear differential equations on Banach spaces, Studia Math. 88 (1988), 37-42. Zbl0639.34050
29. [29] Yu. I. Lyubich and Vũ Quôc Phóng, A spectral criterion for almost periodicity of one-parameter semigroups, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 47 (1987), 36-41 (in Russian). 
30. [30] Yu. I. Lyubich and Vũ Quôc Phóng, A spectral criterion for almost periodicity of representations of abelian semigroups, ibid. 51 (1987) (in Russian). 
31. [31] R. Nagel and F. Räbiger, Superstable operators on Banach spaces, Israel J. Math. 81 (1993), 213-226. Zbl0788.47003
32. [32] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970. Zbl0201.45003
33. [33] D. J. Newman, Simple analytic proof of the prime number theorem, Amer. Math. Monthly 87 (1980), 693-696. Zbl0444.10033
34. [34] G. K. Pedersen, C*-Algebras and Their Automorphism Groups, Academic Press, London, 1979. Zbl0416.46043
35. [35] Vũ Quôc Phóng, Theorems of Katznelson-Tzafriri type for semigroups of operators, J. Funct. Anal. 103 (1992), 74-84. Zbl0770.47017
36. [36] G. M. Sklyar and V. Ya. Shirman, On the asymptotic stability of a linear differential equation in a Banach space, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 37 (1982), 127-132 (in Russian). Zbl0521.34063
37. [37] G. Stolzenberg, Polynomially and rationally convex sets, Acta Math. 109 (1963), 259-289. Zbl0122.08404
38. [38] E. L. Stout, The Theory of Uniform Algebras, Bogden & Quigley, Tarrytown-on-Hudson, 1971. Zbl0286.46049
39. [39] J. Wermer, Banach Algebras and Several Complex Variables, Springer, New York, 1976. 
40. [40] W. Żelazko, On a certain class of non-removable ideals in Banach algebras, Studia Math. 44 (1972), 87-92. Zbl0213.40603

1. C. Batty, Some Tauberian theorems related to operator theory
2. Yu. Tomilov, On the spectral bound of the generator of a $C_0$-semigroup
3. Olavi Nevanlinna, On the growth of the resolvent operators for power bounded operators
4. Zoltán Léka, A note on the powers of Cesàro bounded operators
5. Vũ Phóng, Almost periodic and strongly stable semigroups of operators
6. Driss Drissi, On a theorem of Gelfand and its local generalizations
7. Adam Bobrowski, A note on convergence of semigroups
8. Jaroslav Zemánek, On the Gelfand-Hille theorems