Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces

Ryotaro Sato

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 1, page 77-88
  • ISSN: 0010-2628

Abstract

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We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces.

How to cite

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Sato, Ryotaro. "Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 52.1 (2011): 77-88. <http://eudml.org/doc/246817>.

@article{Sato2011,
abstract = {We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces.},
author = {Sato, Ryotaro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ratio Tauberian theorem; $\gamma $-th order Cesàro integral; Laplace integral; $\gamma $-th order Cesàro sum; Abel sum; ratio Tauberian theorem; -th order Cesàro integral; Laplace integral; -th order Cesàro sum; Abel sum},
language = {eng},
number = {1},
pages = {77-88},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces},
url = {http://eudml.org/doc/246817},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Sato, Ryotaro
TI - Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 1
SP - 77
EP - 88
AB - We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces.
LA - eng
KW - ratio Tauberian theorem; $\gamma $-th order Cesàro integral; Laplace integral; $\gamma $-th order Cesàro sum; Abel sum; ratio Tauberian theorem; -th order Cesàro integral; Laplace integral; -th order Cesàro sum; Abel sum
UR - http://eudml.org/doc/246817
ER -

References

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  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. MR1886588
  2. Chen J.-C., Sato R., 10.1016/j.jmaa.2009.12.047, J. Math. Anal. Appl. 367 (2010), 108–115. Zbl1194.40004MR2600382DOI10.1016/j.jmaa.2009.12.047
  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. MR2674604
  4. Emilion R., 10.1016/0022-1236(85)90037-0, J. Funct. Anal. 61 (1985), 1–14. Zbl0562.47007MR0779737DOI10.1016/0022-1236(85)90037-0
  5. Li Y.-C., Sato R., Shaw S.-Y., 10.1007/s11856-007-0091-x, Israel J. Math. 162 (2007), 109–149. Zbl1142.40002MR2365856DOI10.1007/s11856-007-0091-x
  6. Li Y.-C., Sato R., Shaw S.-Y., 10.1007/s11117-007-2085-7, Positivity 11 (2007), 433–447. Zbl1127.40003MR2336207DOI10.1007/s11117-007-2085-7
  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. Zbl0219.44001
  9. Zygmund A., Trigonometric Series. Vol. I, Cambridge University Press, Cambridge, 1959. Zbl0367.42001MR0107776

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