On Algebraicity of Global Real Analytic Sets and Functions
On approximating submanifolds by algebraic sets and a solution to the Nash conjecture.
On Equivalence of Ideals of Real Global Analytic Functions and the 17th Hilbert Problem.
On normalization of Nash varieties
On the extension of Nash functions.
On the group of real analytic diffeomorphisms
The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.
On the Real Spectrum of a Ring of Global Analytic Functions
On the relative Nash approximation of analytic maps.
On the uniqueness of the analyticity of a proper G-action.
Petites valeurs propres et classe d’Euler des fibrés
Real Algebraic Geometry and the 17th Hilbert Problem.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Separation, factorization and finite sheaves on Nash manifolds
Some Remarks on Analytic Foliations and Analytic Branched Coverings.
Sur certains sous-ensembles de l'espace euclidien
Soit l’algèbre des fonctions sur engendrée par les fonctions polynomiales et les exponentielles de formes linéaires. La partie de appartient à si et seulement s’il existe et dans pour lesquels est l’image par la projection canonique de sur , de l’ensemble des zéros de . Soit le plus petit sous-ensemble de parties de qui contient , l’adhérence de ses éléments et les images par la projection canonique de qui contient , l’adhérence de ses éléments et les images par la...
Teoremi di approssimazione per gli spazi analitici reali coerenti non immergibili in
The Gaussian measure on algebraic varieties
We prove that the ring ℝ[M] of all polynomials defined on a real algebraic variety is dense in the Hilbert space , where dμ denotes the volume form of M and the Gaussian measure on M.
The homotopy axiom in semialgebraic cohomology.
Усиление теоремы Нэша-Тониоли