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Journal of the London Mathematical Society 2000 62(1):253-262; doi:10.1112/S0024610700001174
© 2000 by London Mathematical Society
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© The London Mathematical Society

Hypercyclic and Chaotic Convolution Operators

José Bonet

Departamento de Matemática Aplicada, Universidad Politécnica de Valencia E-46071 Valencia, Spain, jbonet{at}pleiades.upv.es

Received 8 September 1998. Revision received 21 April 1999.

Every convolution operator on a space of ultradifferentiable functions of Beurling or Roumieu type and on the corresponding space of ultradistributions is hypercyclic and chaotic when it is not a multiple of the identity. The operator of differentiation is hypercyclic on the space A–{infty}, but it need not be hypercyclic on radial weighted algebras of entire functions.


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