Hypercyclic convolution operators on Fréchet spaces of analytic functions

CARANDO, DANIEL; DIMANT, VERÓNICA; MURO, SANTIAGO

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2007 vol. 336 p. 1324 - 1340

0022-247X

A result of Godefroy and Shapiro states that the convolutionoperators on the space of entire functions on $mathbb C^n$, whichare not multiples of identity, are hypercyclic. Analogues of thisresult have appeared for some spaces of holomorphic functions on aBanach space. In this work, we define the space holomorphicfunctions associated to a sequence of spaces of polynomials anddetermine conditions on this sequence that assure hypercyclicity ofconvolution operators. Some known results come out as particularcases of this setting. We also consider holomorphic functionsassociated to minimal ideals of polynomials and to polynomials ofthe Schatten-von Neumann class.