Boundedness and growth orders of means of discrete and continuous semigroups of operators

Tom 187 / 2008

Yuan-Chuan Li, Ryotaro Sato, Sen-Yen Shaw Studia Mathematica 187 (2008), 1-35 MSC: 40E10, 47A35, 47D06. DOI: 10.4064/sm187-1-1

Streszczenie

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.

Autorzy

  • Yuan-Chuan LiDepartment of Applied Mathematics
    National Chung-Hsing University
    Taichung, 402 Taiwan
    e-mail
  • Ryotaro SatoDepartment of Mathematics
    Okayama University
    Okayama, 700-8530 Japan
    and
    19-18 Higashi-hongo 2-chome
    Midori-ku
    Yokohama, 226-0002 Japan
    e-mail
  • Sen-Yen ShawGraduate School of Engineering
    Lunghwa University of Science and Technology
    Gueishan, Taoyuan, 333 Taiwan
    e-mail

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