ON QUASIANALYTIC LOCAL RINGS

By Vincent Thilliez. 2005

90 citations recorded by the source corpus.

Abstract This expository article is devoted to the local theory of ultradifferentiable classes of functions, with a special emphasis on the quasianalytic case. Although quasianalytic classes are well-known in harmonic analysis since several decades, their study from the viewpoint of differential analysis and analytic geometry has begun much more recently and, to some extent, has earned them a new interest. Therefore, we focus on contemporary questions closely related to topics in local algebra. We study, in particular, Weierstrass division problems and the role of hyperbolicity, together with properties of ideals of quasianalytic germs. Incidentally, we also present a simplified proof of Carleman's theorem on the non-surjectivity of the Borel map in the quasianalytic case.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7cef150b4d0ce736ba2c6f7418316bb5849b407b

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In Applied Mathematics

1. A. Rainer
2. Peter W. Michor
3. Andreas Kriegl
4. B. Clarke

In Geometry and Topology

1. A. Rainer
2. Peter W. Michor
3. Andreas Kriegl
4. B. Clarke

In Mathematical Physics

1. A. Rainer
2. Peter W. Michor
3. Andreas Kriegl
4. Tom Leinster
5. Michel Waldschmidt
6. B. Clarke

Citations in the corpus

• The convenient setting for non-quasianalytic Denjoy–Carleman differentiable mappings☆ (2008, methodology): “In the description of C M ρ (K), instead of compact K with smooth boundary, we may also use open K ⊂ U with K compact in U , like [27].”