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|Title:||Hypercyclic Convolution Operators On Spaces Of Entire Functions|
Vinicius V.; Mujica
|Abstract:||A classical result of Birkhoff states that every nontrivial translation operator on the space H (C) of entire functions of one complex variable is hypercyclic. Godefroy and Shapiro extended this result considerably by proving that every nontrivial convolution operator on the space H (C-n) of entire functions of several complex variables is hypercyclic. In sharp contrast with these classical results we show that no convolution operator on the space H (C-N) of entire functions of infinitely many complex variables is hypercyclic. On the positive side we obtain hypercyclicity results for convolution operators on spaces of entire functions on important locally convex spaces.|
Locally Convex Spaces
|Citation:||Journal Of Operator Theory. Theta Foundation, v. 76, p. 141 - 158, 2016.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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