Expressing as a difference of two positive functions
Extending Hardy fields by non--germs
For a large class of Hardy fields their extensions containing non--germs are constructed. Hardy fields composed of only non--germs, apart from constants, are also considered.
Extending Tamm's theorem
We extend a result of M. Tamm as follows:Let , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions . Then there exists such that for all , if is in a neighborhood of , then is real analytic in a neighborhood of .
Extension of functions from sets with polynomial cusps
Extensions de jets dans des intersections de classes non quasi-analytiques
In [3], J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset E of ℝⁿ, in the case of intersections of non-quasi-analytic classes with moderate growth and a Łojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every -Whitney jet belongs to one of them. We also prove a linear extension theorem...
Extreme values of integrals of some bell shaped classes of functions
Fourier series. Fourier transforms and applications.
Funciones con derivadas sucesivas grandes y pequeñas por doquier.
Holomorphic extension of a function whose odd derivatives are summable
Inclusion and differentiability criteria for Lp-classes of infinitely differentiable functions.
Inégalités de Łojasiewicz globales
On étudie les propriétés métriques des ensembles analytique réels , avec , algèbre analytique topologiquement noethérienne. Ainsi, on construit de larges classes d’algèbres topologiquement noethériennes et vérifiant des conditions de Łojasiewicz globales d’un certain type. Comme application, on obtient des théorèmes de division de fonction par des fonctions analytiques.
Infinitely Differentiable Functions With Prescribed Derivatives At A Point.
Interpolation and extrapolation of smooth functions by linear operators.
Interpolation Gevrey dans les domaines de type fini de C2.
Local properties of maps of the ball.
Łojasiewicz ideals in Denjoy-Carleman classes
The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the case have a Denjoy-Carleman counterpart.
Markov's Inequality and C Functions on Sets with Polynomial Cusps.
Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods
We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces...
On a problem concerning quasianalytic local rings
Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let and f̂ be its Taylor series at . Split the set of exponents into two disjoint subsets A and B, , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some m ≥ 2, then...
On alternative functional equations. (Short Communication).