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2 results

  • The Initial and Terminal Cluster Sets of an Analytic Curve

  • Paul M. Gauthier
  • Journal:
    Canadian Mathematical Bulletin / Volume 61 / Issue 2 / 01 June 2018
    Published online by Cambridge University Press:
    20 November 2018, pp. 282-288
    Print publication:
    01 June 2018
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  • For an analytic curve $\gamma :\,\left( a,\,b \right)\,\to \,\mathbb{C}$, the set of values approached by $\gamma \left( t \right)$, as $t\,\searrow \,\,a$ and as $t\,\nearrow \,b$ can be any two continua of $\mathbb{C}\,\cup \,\left\{ \infty \right\}$.

  • BOUNDARY-CHAOTIC BEHAVIOUR OF CONTINUOUS FUNCTIONS UNDER THE ACTION OF OPERATORS

  • Luis Bernal-González, María del Carmen Calderón-Moreno
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 46 / Issue 2 / June 2003
    Published online by Cambridge University Press:
    04 July 2003, pp. 451-464
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  • In this paper we introduce two classes of operators on spaces of continuous functions with values in $F$-spaces under the action of which many functions behave chaotically near the boundary. Several examples—including onto linear operators, left and right composition operators, multiplication operators, and operators with pointwise dense range or with some stability property—are given. This new theory extends one recently developed on spaces of holomorphic functions.

    AMS 2000 Mathematics subject classification: Primary 47B38. Secondary 30D40; 46E10; 54D45