Failure of the Weierstrass Preparation Theorem in Quasi-analytic Denjoy-Carleman Rings

Speaker: A. Nicoara (UCD)

Date: Tuesday, 29th September 2015

Time: 3.30pm

Location: Trinity College, WR20

Abstract:

In 1976 Childress proved Weierstrass Division failed in quasi-analytic Denjoy-Carleman rings. While Weierstrass Division implies the Weierstrass Preparation Theorem, the reverse is not known to hold. The question of whether the Weierstrass Preparation Theorem held for Denjoy-Carleman functions or not remained open for over 30 years. In joint work with Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein, and Nahum Zobin, we showed the Weierstrass Preparation Theorem fails for Denjoy-Carleman functions by proving a strong non-extension result.

Series: Analysis