This paper investigates hyperbolic polynomials with quasianalytic coefficients. Our main purpose is to prove factorization theorems for such polynomials, and next to generalize the results of K. Kurdyka and L. Paunescu about perturbation of analytic families of symmetric matrices to the quasianalytic setting.
We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson’s Lemma under an additional condition related to the growth index of the sequence.
Nous proposons une généralisation d’un résultat de F. Berteloot et G. Patrizio [1], aux cas des applications holomorphes propres entre domaines quasi-disqués et non nécessairement bornés.
We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.
This is a survey (including new results) of relations ?some emergent, others established? among three notions which the 1980s saw introduced into knot theory: quasipositivity of a link, the enhanced Milnor number of a fibered link, and the new link polynomials. The Seifert form fails to determine these invariants; perhaps there exists an ?enhanced Seifert form? which does.
Un résultat de positivité de théorie de Hodge nous permet de déterminer certaines pôles de la distribution pour une fonction analytique à singularité isolée. Dans le cas des courbes et des singularités quasi-homogènes on détermine l’ensemble exact des pôles. On démontre aussi que si le résidu d’une forme holomorphe est de carré intégrable sur la fibre spéciale, l’intégrale sur la fibre spéciale est limite de celle sur les fibres voisines.