| Full text | |
| Author(s): |
Favaro, Vinicius V.
;
Mujica, Jorge
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF OPERATOR THEORY; v. 76, n. 1, p. 141-158, SUM 2016. |
| Web of Science Citations: | 4 |
| 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. (AU) | |
| FAPESP's process: | 14/50536-7 - Spaces of holomorphic functions defined on Banach spaces and the Michael’s problem |
| Grantee: | Vinícius Vieira Fávaro |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |