Quantization in complex analysis and operator theory
 
 
Description: 

In this talk it will be explored the relevance of quantization on the construction of polyanalytic function spaces likewise its relevance on the study of class of Toeplitz operators obtained from Berezin quantization.

Starting from a group representation for the Heisenberg group <i>\mathbb{H}</i>, it will be shown the relevance of the symmetries of the metaplectic group <i>\widetilde{Sp(2)}</i> (the so-called Shale-Weil representation) and moreover the relevance of the symmetries of <i>\mathbb{H}\rtimes\widetilde{Sp(2)}</i> in the construction of polyanalytic Fock spaces <i>{\bf F}<sup>n(\mathbb{C})</sup></i> of order <i>n</i> on the complex plane <i>\mathbb{C}</i> likewise polyanalytic Bergmann spaces <i>{\bf A}<sup>n</sup><sub>\alpha(\mathbb{D})</sub></i> of order <i>n</i> (<i>\alpha\geq 0</i>) on a Siegel disk <i>\mathbb{D}</i>.

Afterwards, we will construct families of coherent states from the polyanalytic function space <i>{\bf F}<sup>n(\mathbb{C})</sup></i> resp. <i>{\bf A}<sup>n</sup><sub>\alpha(\mathbb{D})</sub></i>, and moreover, families of Toeplitz operators regarding these function spaces.

Date:  2012-02-17
Start Time:   14:30
Speaker:  Nelson Faustino (CMUC)
Institution:  CMUC
Place:  Sala 5.5
Research Groups: -Analysis
See more:   <Main>  
 
© Centre for Mathematics, University of Coimbra, funded by
Science and Technology Foundation
Powered by: rdOnWeb v1.4 | technical support