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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 1
- .......... Page(s) .......... 9
- .......... Page(s) .......... 9
- We characterize the classes
M (I) and (I) which are inverse-closed by showing that the condition given by Paul Malliavin [1] for such a class to be inverse-closed is also necessary - .......... Page(s) .......... 13
- .......... Page(s) .......... 17
- We prove that semilinear hyperbolic systems in two variables, whose nonlinear term satisfies a global Lipschitz condition, admit global generalized solutions in the Colombeau algebra for initial data arbitrary distributions. These solutions are unique and consistent with the classical or distributional solutions, when they exist.
- .......... Page(s) .......... 19
- J. Leray [6], and L. Garding, T. Kotake and J. Leray [2] have studied the singularities of the solution of the linear Cauchy problem with holomorphic data, when the initial surface has characteristic points. Y. Choquet-Bruhat [1] has extended certain results of [6], [2] to the case of a system of nonlinear equations. In this Note, following the reasonings of [6], [2], we give a complement of certain results of [6], [2] in the case of the operators with multiple characteristics.
- .......... Page(s) .......... 23
- .......... Page(s) .......... 23
- We define the index Index E of a conditional expectation E: B A on a simple C*-algebra B. If Index E<4, then it must be 4 cos2 (/n) for some integer n. We establish the link between the transfer in K-theory and the multiplication map by Index E.
- .......... Page(s) .......... 27
- .......... Page(s) .......... 27
- We identify two cohomologies associated with the "transverse structure" of a regular foliation (M, F): the one of the QF-manifold S=M/F induced by the foliation [1] and the one of the classifying space of the total holonomy pseudogroup on a transverse submanifold (C. Godbillon [3]). Considering the canonical QF-submersion p: M S and calling "transverse classes" the elements of the inverse image by p of the cohomology of S, we prove that the characteristic classes introduced by A. Haefliger [2] are transverse.
- .......... Page(s) .......... 31
- .......... Page(s) .......... 31
- Let E, F, G be finite dimensional vector spaces, a semi-martingale with values in C (E; F), a semi-martingale with values in C (F; G), X a semi-martingale with values in E. We prove the following three theorems: 1. (X) is a semi-martingale with values in F; 2. is a semi-martingale with values in C (E; G); 3. If is inversible, -1 is a semi-martingale with values in C (F; E). This theorem 3 will be proved only in a further Note (II).
- .......... Page(s) .......... 37
- We give some improvements of the ratio inequalities obtained by M. Yor and independently by R. Gundy for continuous martingales.
- MATHEMATIQUE 1987 - Tome 305 - Série I - n° 1
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