On quasianalytic local rings
From MaRDI portal
Publication:2473998
DOI10.1016/j.exmath.2007.04.001zbMath1139.32003arXivmath/0509273OpenAlexW3100152083MaRDI QIDQ2473998
Publication date: 5 March 2008
Published in: Expositiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0509273
local algebrasDenjoy-Carleman classesclosed idealsWeierstrass division propertyBorel's extension theorem
(C^infty)-functions, quasi-analytic functions (26E10) Rings and algebras of continuous, differentiable or analytic functions (46E25) Analytic algebras and generalizations, preparation theorems (32B05)
Related Items
Equality of ultradifferentiable classes by means of indices of mixed O-regular variation ⋮ Estimates for Weierstrass division in ultradifferentiable classes ⋮ On a problem concerning the ring of Nash germs and the Borel mapping ⋮ How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes? ⋮ On the maximal extension in the mixed ultradifferentiable weight sequence setting ⋮ Polynomial inequalities, o-minimality and Denjoy-Carleman classes ⋮ Composition in ultradifferentiable classes ⋮ Ultradifferentiable Chevalley theorems and isotropic functions ⋮ A generalization of Puiseux's theorem and lifting curves over invariants ⋮ Lagrangian regularity of the electron magnetohydrodynamics flow on a bounded domain ⋮ Solutions of quasianalytic equations ⋮ The theorem of iterates for elliptic and non-elliptic operators ⋮ Ultradifferentiable extension theorems: a survey ⋮ An interpolation problem in the Denjoy–Carleman classes ⋮ Ultradifferentiable CR manifolds ⋮ Functions with ultradifferentiable powers ⋮ Ultradifferentiable classes of entire functions ⋮ On generalized definitions of ultradifferentiable classes ⋮ The Abhyankar-Jung theorem ⋮ Monomialization of a quasianalytic morphism ⋮ The exponential law for spaces of test functions and diffeomorphism groups ⋮ Geometric microlocal analysis in Denjoy-Carleman classes ⋮ The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings ⋮ Unnamed Item ⋮ Failure of the Weierstrass preparation theorem in quasi-analytic Denjoy-Carleman rings ⋮ The convenient setting for Denjoy-Carleman differentiable mappings of Beurling and Roumieu type ⋮ A constructive approach to regularity of Lagrangian trajectories for incompressible Euler flow in a bounded domain ⋮ Generic results in classes of ultradifferentiable functions ⋮ Smooth solutions of quasianalytic or ultraholomorphic equations ⋮ Newton polyhedra and weighted oscillatory integrals with smooth phases ⋮ A global Nullstellensatz for ideals of Denjoy-Carleman functions ⋮ Fourier analysis for Denjoy–Carleman classes on the torus ⋮ Extension of Bochnak-Siciak theorem for smooth Denjoy-Carleman functions ⋮ On the Siegel-Sternberg linearization theorem ⋮ Hamiltonian perturbation theory for ultra-differentiable functions ⋮ On the construction of large algebras not contained in the image of the Borel map ⋮ Invariant functions in Denjoy-Carleman classes ⋮ Quasianalytic multiparameter perturbation of polynomials and normal matrices ⋮ The convenient setting for non-quasianalytic Denjoy-Carleman differentiable mappings ⋮ On the surjectivity of the Borel mapping for some quasi-analytic rings ⋮ Perturbation theory for normal operators ⋮ Composite quasianalytic functions ⋮ Quantifier elimination in quasianalytic structures via non-standard analysis
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A sharp division estimate for ultradifferentiable germs.
- On E. Borel's theorem
- The implicit function theorem for ultradifferentiable mappings
- Sur les exposants de Lojasiewicz
- Characterization of Noetherian rings of formal power series with controlled growth. Application to spectral synthesis
- UPC condition in polynomially bounded o-minimal structures
- Smooth submanifolds intersecting any analytic curve in a discrete set
- Resolution of singularities in Denjoy-Carleman classes
- On certain extension theorems in the mixed Borel setting
- Ultra-distributions definies sur \(R^ n\) et sur certaines classes de variétés différentiables
- Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
- Weierstrass Division in Quasianalytic Local Rings
- Quasianalytic Denjoy-Carleman classes and o-minimality
- Bounds for quotients in rings of formal power series with growth constraints
- Division par un polynôme hyperbolique
- Quasianalyticity and pluripolarity
- Sur le théorème de division de Weierstrass