Geodesic
Boundedness and growth orders of means of discrete and continuous semigroups of operators
Yuan-Chuan Li1 ; Ryotaro Sato2 ; Sen-Yen Shaw3
1Department of Applied Mathematics National Chung-Hsing University Taichung, 402 Taiwan
2Department of Mathematics Okayama University Okayama, 700-8530 Japan and 19-18 Higashi-hongo 2-chome Midori-ku Yokohama, 226-0002 Japan
3Graduate School of Engineering Lunghwa University of Science and Technology Gueishan, Taoyuan, 333 Taiwan
Studia Mathematica, Tome 187 (2008) no. 1, pp. 1-35
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We discuss implication relations for boundedness and growth orders of Cesàro means and Abel means of discrete semigroups and continuous semigroups of linear operators. Counterexamples are constructed to show that implication relations between two Cesàro means of different orders or between Cesàro means and Abel means are in general strict, except when the space has dimension one or two.
DOI : 10.4064/sm187-1-1
Keywords: discuss implication relations boundedness growth orders ces means abel means discrete semigroups continuous semigroups linear operators counterexamples constructed implication relations between ces means different orders between ces means abel means general strict except space has dimension

Yuan-Chuan Li  1   ; Ryotaro Sato  2   ; Sen-Yen Shaw  3

1 Department of Applied Mathematics National Chung-Hsing University Taichung, 402 Taiwan
2 Department of Mathematics Okayama University Okayama, 700-8530 Japan and 19-18 Higashi-hongo 2-chome Midori-ku Yokohama, 226-0002 Japan
3 Graduate School of Engineering Lunghwa University of Science and Technology Gueishan, Taoyuan, 333 Taiwan 
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Yuan-Chuan Li; Ryotaro Sato; Sen-Yen Shaw. Boundedness and growth orders of means of discrete and
 continuous semigroups of operators. Studia Mathematica, Tome 187 (2008) no. 1, pp. 1-35. doi: 10.4064/sm187-1-1

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