Beurling's method in the theory of quasianalytic functions

Mon, 03/11/2014 - 14:00

The talk is will be devoted to two  questions in the theory of quasianalytic  
Carleman classes. The first one is how to describe the image of a quasianalytic 
Carleman class under Borel's map $f\to\{f^{(n)}(0)/n!\}_{n\geq 0}$ ?    
The second one is how to sum the formal Taylor series of functions  in quasianalytic Carleman classes? In the talk, I will present a method of Beurling that gives a solution to both of the problems for some quasianalytic Carleman classes. If time permits, I will also discuss the image problem in some non-quasianalytic classes.