Research Communication | Open Access
Volume 2019 | Communication ID 110
Volume 2019 | Communication ID 110
| Strong mixing Gaussian measures for chaotic semigroups |
Mohamed Chakir, El Mourchid Samir
Received |
Accepted |
Published |
Jan 26, 2019 |
Feb 26, 2019 |
Mar 01, 2019 |
Abstract: In this talk, we will be concerned with the problem of the existence of an invariant mixing measure considering its connection with the chaotic behavior of linear semigroups on separable Banach spaces. We prove an identity characterizing invariant Gaussian measure involving its covariance operator and the infinitesimal generator of the semigroup. This gives an answer to a question raised by Rudnicki in his inspiring review paper [1]. we use the proved identity to give an another proof to Bayert theorem for the existence of an invariant mixing Gaussian measure [2].