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2 results

  • Recurrence of Cosine Operator Functions on Groups

  • Chung-Chuan Chen
  • Journal:
    Canadian Mathematical Bulletin / Volume 59 / Issue 4 / 01 December 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 693-704
    Print publication:
    01 December 2016
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  • In this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.

  • Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions

  • Jamil A. Siddiqi, Abdelkader Elkoutri
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 1 / 01 March 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 47-53
    Print publication:
    01 March 1989
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  • We prove that if A is the infinitesimal generator of a bounded analytic semigroup in a sector {z ∊ C : |arg z| ≦ (απ)/2} of bounded linear operators on a Banach space, then the following inequalities hold:

    for any x ∊ D(An) and for any 0 < β < α. This result helps us to answer in affirmative a question raised by M. W. Certain and T. G. Kurtz [3]. Similar inequalities are proved for cosine operator funtions.