Sequences of differential operators: exponentials, hypercyclicity and equicontinuity

Tom 77 / 2001

L. Bernal-González, J. A. Prado-Tendero Annales Polonici Mathematici 77 (2001), 169-187 MSC: Primary 47B38; Secondary 30E10, 47A16, 47E05, 47F05. DOI: 10.4064/ap77-2-4

Streszczenie

An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of ${\mathbb C}^N$ are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is ${\mathbb C}^N$. The results obtained extend or improve earlier work of several authors.

Autorzy

  • L. Bernal-GonzálezDepartamento de Análisis Matemático
    Facultad de Matemáticas, Apdo. 1160
    Avenida Reina Mercedes
    41080 Sevilla, Spain
    e-mail
  • J. A. Prado-TenderoDepartamento de Análisis Matemático
    Facultad de Matemáticas, Apdo. 1160
    Avenida Reina Mercedes
    41080 Sevilla, Spain
    e-mail

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