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- CONTENTS 1985 - VOLUME 300 - SECTION I - N° 18
- .......... Page(s) .......... 621
- .......... Page(s) .......... 621
- We consider finite energy solutions of the perturbed wave equation with "impurities" which depend upon space and time with , , in the case
. We prove that under suitable assumptions on the potential q(x, t), the scattering operator exists and we analyse some of its properties. Finally, we present a result on the uniqueness of the inverse scattering problem associated to the above equation in the case n=3.
- .......... Page(s) .......... 625
- .......... Page(s) .......... 625
- We generalize the classical theory of amenable locally compact groups to Kac algebras. Most of the equivalent definitions of amenability are translated into the formalism of Kac algebras and still remain equivalent. Among others, we see that every "group dual" (i. e. symmetric Kac algebra) is amenable. Results on actions of amenable groups on van Neumann algebras are extended as well; this allows us to obtain new properties on group co-actions (i. e. actions of "group duals").
- .......... Page(s) .......... 631
- Neutral manifold endowed with a conformal symplectic structure and coisotropic foliation, Radu Rosca.......... Page(s) .......... 631
- Necessary and sufficient condition for the fundamental 2-form to be conformal symplectic is given and certain infinitesimal transformations with respect to this structure are discussed. If Fc is a coisotropic foliation on , then the leaves Mc of Fc are CR submanifolds of with involutive and isotropic vertical distribution.
- .......... Page(s) .......... 635
- .......... Page(s) .......... 635
- We introduce the notion of regular open sets for C°-codimension one foliations of a compact manifold with a transverse one-dimensional foliation. These open sets have a simple characterization in terms of local minimal sets of these foliations and the complementary of their union consists of finitely many closures of half-proper leaves. These leaves are attracting in a proper side.
- In class C2, we obtain some stability properties of proper leaves.
- .......... Page(s) .......... 639
- As a continuation of a former Note [10] on the fundamental groupoid of a foliation , this one aims to exhibit a canonical isomorphism between and a full subgroupoid of the Poincaré groupoid of the classifying space of the holonomy groupoid of . This is a peculiar case of a relation, asserted by van Est, between the fundamental group of a S-atlas (P, T) and that of the classifying space of T.
- .......... Page(s) .......... 643
- .......... Page(s) .......... 643
- The function is shown to be exact Hausdorff measure function for the range of a transient Levy Brownian motion process with multidimensional time. This result settles a question asked by P. Levy in [11] and [12]. The main tool is a projection Lemma (of independent interest) based on McKean's decomposition of Brownian motion.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES MATHEMATIQUE 1985 - Tome 300 - Série I - n° 18
- Analyse mathématique
- .......... Page(s) .......... 617
- Equations aux dérivées partielles
- .......... Page(s) .......... 621
- Analyse fonctionnelle
- .......... Page(s) .......... 625
- Géométrie algébrique
- .......... Page(s) .......... 627
- Géométrie différentielle
- Variétés neutres admettant une structure conforme symplectique et feuilletage coisotrope. Radu Rosca.......... Page(s) .......... 631
- Topologie différentielle
- .......... Page(s) .......... 635
- .......... Page(s) .......... 639
- Probabilités
- .......... Page(s) .......... 643
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