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Hypercyclic and Chaotic Convolution Operators
Author(s) -
Bonet José
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001174
Subject(s) - convolution (computer science) , chaotic , mathematics , operator (biology) , entire function , space (punctuation) , pure mathematics , convolution power , identity (music) , type (biology) , circular convolution , mathematical analysis , computer science , physics , artificial intelligence , fourier transform , fourier analysis , repressor , chemistry , acoustics , operating system , biochemistry , artificial neural network , transcription factor , fractional fourier transform , gene , ecology , biology
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 −∞ , but it need not be hypercyclic on radial weighted algebras of entire functions.