Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
ratio Tauberian theorem; $\gamma$-th order Cesàro integral; Laplace integral; $\gamma$-th order Cesàro sum; Abel sum
ratio Tauberian theorem; $\gamma$-th order Cesàro integral; Laplace integral; $\gamma$-th order Cesàro sum; Abel sum
Summary:
We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces.
References:
[1] Arendt W., Batty C.J.K., Hieber M., Neubrander F.: Vector-valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics Vol. 96, Birkhäuser, Basel, 2001. MR 1886588
[2] Chen J.-C., Sato R.: Ratio limit theorems and Tauberian theorems for vector-valued functions and sequences. J. Math. Anal. Appl. 367 (2010), 108–115. DOI 10.1016/j.jmaa.2009.12.047 | MR 2600382 | Zbl 1194.40004
[3] Chen J.-C., Sato R., Shaw S.-Y.: Growth orders of Cesàro and Abel means of functions in Banach spaces. Taiwanese J. Math. 14 (2010), 1201–1248. MR 2674604
[4] Emilion R.: Mean-bounded operators and mean ergodic theorems. J. Funct. Anal. 61 (1985), 1–14. DOI 10.1016/0022-1236(85)90037-0 | MR 0779737 | Zbl 0562.47007
[5] Li Y.-C., Sato R., Shaw S.-Y.: Convergence theorems and Tauberian theorems for functions and sequences in Banach spaces and Banach lattices. Israel J. Math. 162 (2007), 109–149. DOI 10.1007/s11856-007-0091-x | MR 2365856 | Zbl 1142.40002
[6] Li Y.-C., Sato R., Shaw S.-Y.: Ratio Tauberian theorems for positive functions and sequences in Banach lattices. Positivity 11 (2007), 433–447. DOI 10.1007/s11117-007-2085-7 | MR 2336207 | Zbl 1127.40003
[7] Sato R.: On means of Banach-space-valued functions. Math. J. Okayama Univ.(to appear).
[8] Widder D.V.: An Introduction to Transform Theory. Academic Press, New York and London, 1971. Zbl 0219.44001
[9] Zygmund A.: Trigonometric Series. Vol. I. Cambridge University Press, Cambridge, 1959. MR 0107776 | Zbl 0367.42001
Search
Partner of
