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Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second, the tempered-stratified...

Subanalytic version of Whitney's extension theorem

Krzysztof Kurdyka, Wiesław Pawłucki (1997)

Studia Mathematica

For any subanalytic C k -Whitney field (k finite), we construct its subanalytic C k -extension to ℝ n . Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.

Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity

Andrei A. Agrachev, Andrei V. Sarychev (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...

Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices" (Ann. Polon. Math. 101 (2011), 275-291)

Krzysztof Jan Nowak (2012)

Annales Polonici Mathematici

In IMUJ Preprint 2009/05 we investigated the quasianalytic perturbation of hyperbolic polynomials and symmetric matrices by applying our quasianalytic version of the Abhyankar-Jung theorem from IMUJ Preprint 2009/02, whose proof relied on a theorem by Luengo on ν-quasiordinary polynomials. But those papers of ours were suspended after we had become aware that Luengo's paper contained an essential gap. This gave rise to our subsequent article on quasianalytic perturbation theory, which developed,...

Sur la dualité locale

Marcos Sebastiani (1980)

Annales de l'institut Fourier

Une construction explicite et élémentaire de l’homomorphisme trace pour les applications analytiques locales de type fini entre des espaces normaux est donnée. On généralise le théorème de dualité locale dans le cas où l’anneau local à la source est un anneau de factorisation unique. Des exemples et des applications sont donnés.

Sur le théorème de division de Weierstrass

Jacques Chaumat, Anne-Marie Chollet (1995)

Studia Mathematica

We prove a Weierstrass division formula for C ∞ Whitney jets ∂̅-flat on arbitrary compact subsets of the complex plane. We also give results for Carleman classes.

Currently displaying 21 – 40 of 49