The talk is will be devoted to two questions in the theory of quasianalytic Beurling classes. The first one is how to describe the image of a quasianalytic Beurling class under Borel's map f → { f (n)(0) ⁄ n ! }n  ≥  0 ?

The second one is how to sum the formal Taylor series of functions in quasianalytic Beurling classes?

In the talk, I will present a method of Beurling that gives a solution to both of the problems for some quasianalytic Beurling classes. If time permits, I will also discuss the image problem in some non-quasianalytic classes.

Analysis and related topics