Andreea C. Nicoara

ON THE RELATIONSHIP BETWEEN D'ANGELO q-TYPE AND CATLIN q-TYPE

We establish inequalities relating two measurements of the order of contact of

A Nullstellensatz for Łojasiewicz ideals

q

Coherence and other properties of sheaves in the Kohn algorithm

q-dimensional complex varieties with a real hypersurface.

Equivalence of types and Catlin boundary systems

Abstract It is shown that Denjoy–Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a non-extension theorem.

The Kohn Algorithm on Denjoy-Carleman Classes

For an ideal of smooth functions that is either {\L}ojasiewicz or weakly {\L}ojasiewicz, we give a complete characterization of the ideal of functions vanishing on its variety in terms of the global {\L}ojasiewicz radical and Whitney closure. We also prove that the {\L}ojasiewicz radical of such an ideal is analytic-like in the sense that its saturation equals its Whitney closure. This allows us to recover in a different way Nullstellensatz results due to Bochnak and Adkins-Leahy and answer positively a modification of the Nullstellensatz conjecture due to Bochnak.

Sums of squares in pseudoconvex hypersurfaces and torsion phenomena for Catlin's boundary systems.

On a smooth domain in

q

{{\mathbb {C}}^n}