References
Arendt, W. and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc.306 (1988), 837–852.
Arendt, W. and J. Prüss, Vector-valued Tauberian theorems and asymptotic behavior of Volterra equations, SIAM J. Math.23 (1992), 412–448.
Batty, C. J. K.Tauberian theorems for the Laplace Stieltjes transform, Trans. Amer. Math. Soc.322 (1990), 783–804.
Batty, C. J. K. and Vũ Quôc Phóng,Stability of individual elements of one-parameter semigroups, Trans. Amer. Math. Soc.322 (1990), 805–818.
Ingham, A. E.On Wiener's method in Tauberian theorems, Proc. London Math. Soc. (2)38 (1933), 458–480.
Korevaar, J.On Newman's quick way to the prime number theorem, Math. Intelligencer4 (1982), 108–115.
Krengel, U.. Ergodic Theorems, de Gruyter, Berlin 1985.
Nagel, R. One-parameter Semigroups of Positive Operators, Lecture Notes Math.1184, Springer-Verlag 1986.
Nagel, R.,Towards a “matrix theory” for unbounded operator matrices, Math. Z.201 (1989), 57–68.
Vũ Quôc Phóng,The operator equation AX−XB=C with unbounded operators A and B and related abstract Cauchy problems, Math. Z.208 (1991), 567–588.
Widder, D. V., An Introduction to Transform Theory, Academic Press. New York 1971.
Author information
Authors and Affiliations
Additional information
Communicated by Rainer Nagel
Rights and permissions
About this article
Cite this article
Arendt, W., Batty, C.J.K. A complex Tauberian theorem and mean ergodic semigroups. Semigroup Forum 50, 351–366 (1995). https://doi.org/10.1007/BF02573531
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02573531