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- CONTENTS
- 1987 - VOLUME 305 - SECTION I - N° 3
- Group Theory
- .......... Page(s) .......... 59
- Let
be a subalgebra of the Lie algebra g. Zuckerman has conjectured a duality theorem concerning the derived functors of the functor which associates to a g-module its submodule of -finite vectors. We give a short new proof of this result.
- Mathematical Analysis
- .......... Page(s) .......... 63
- We give necessary and sufficient conditions on a sequence of bounded measures which is vaguely convergent to for to be vaguely convergent to , for all F lipschitzian which possesses an asymptote and is taken in the sense of functions of a measure. An application to the convergence of non linear hyperbolic systems which measures as initial data is given in [1] and [2].
- .......... Page(s) .......... 67
- We construct () such that is absolutely continuous for all b and
- purely singular with respect to the Lebesgue measure (n=1, 2,...).
- Complex Analysis
- .......... Page(s) .......... 71
- Using the differential operator (ddc)n, J.-P. Demailly has defined recently [1] a pluricomplex Green function ga(x), for hyperconvex domains in Cn, and in Cn, and . Such a notion exists in a complex Banach space E, with no reference to differential operators or potential theory, and is obtained as maximal element of some family (F) of plurisubharmonic functions; the construction is given with a finite set of singular points for g. With the same method, an indicatrix function is constructed for each bounded set A in E. For this problem we use for (F) a class which was former investigated [2].
- Harmonic Analysis
- .......... Page(s) .......... 77
- An explicit formula is given for spherical functions on SL (3, H), by means of a differential operator inverting the Abel transform. This inversion formula also yields Harish-Chandra's c function, and the spherical Plancherel formula.
- Analytic Geometry
- .......... Page(s) .......... 81
- Let be a smooth proper map of complex varieties. We compute the curvature of the direct image by of a hermitian holomorphic vector bundle on M, endowed with Quillen's metric. We also get the variation of this metric when one considers two metrics on the fibers of , or an exact sequence of bundles on M.
- Differential Geometry
- .......... Page(s) .......... 85
- Asymptotic geometry of "exceptional" leaves of Anosov foliations of T1S, with S closed hyperbolic surface.
- Probability Theory
- .......... Page(s) .......... 89
- We announce comparison theorems for diffusion processes on (see [6] and [7]). From these theorems we derive upper and lower bounds for the transition probabilities of a diffusion process. These bounds do not depend on the modulus of continuity of the coefficients of the infinitesimal generator of the diffusion process. Our results imply point wise estimates for certain solutions of parabolic differential equations (see [6], § 11). In particular we obtain a generalization of Harnack's inequality proved by Krylov and Safonov [4].
- Statistics
- .......... Page(s) .......... 93
- We established in [6] the weak convergence of the multivariate truncated empirical processes under -mixing conditions for weight functions which vanish on the lower boundary of [0, 1]k+1. In this paper we extend the results under strong mixing conditions and also when the weight functions not only vanish on the lower boundary of [0, 1]k+1 but also on the upper corner of [0, 1]k+1.
- Numerical Analysis
- .......... Page(s) .......... 97
- The approximation of thin shell problems by flat plate elements is very simple to implement and very popular in Scientific Computation. Here, we describe the classical method of Clough and Johnson and, next, we give variational formulations which are convenient for convergence studies.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- .......... Page(s) .......... I
- Théorie des groupes
- .......... Page(s) .......... 59
- Analyse mathématique
- Analyse complexe
- .......... Page(s) .......... 71
- Analyse harmonique
- .......... Page(s) .......... 77
- Géométrie analytique
- .......... Page(s) .......... 81
- Géométrie différentielle
- Probabilités
- .......... Page(s) .......... 89
- Statistique
- Analyse numérique
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