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- CONTENTS
- 1988 - VOLUME 306 - SECTION I - N° 6
- Group Theory
- .......... Page(s) .......... 299
- For and Spin (m) we present an efficient method to compute the decomposition of a tensor product of two irreducible G-modules of highest weights and µ.
- Mathematical Analysis
- .......... Page(s) .......... 305
- On stratified Lie groups, we generalize an optimal version of Sobolev imbeddings theorem including the limit case of Trudinger. In some cases, for instance in Rn, we obtain anisotropic versions of these inequalities.
- Complex Analysis
- .......... Page(s) .......... 309
- We study the behaviour of the multitype of a boundary point, under a proper holomorphic mapping near this point, for special domains. More precisely, let and be two model domains in Cn. Let U and V be two neighborhoods of 0 in Cn. We give necessary and sufficient conditions on the multitype of and at 0, in order that there exist a proper holomorphic mapping u: up to the boundary.
- Partial Differential Equations
- .......... Page(s) .......... 313
- We consider the equation and on , where is a bounded domain in RN with a C2 boundary, and f is a continuous function from to . Under general assumptions on f, we prove that there is a * such that the equation () has no positive solution for .
- .......... Page(s) .......... 317
- We obtain existence and uniqueness for several initial boundary value problem formulations and for nonlinear hyperbolic systems. These results are established for a broad class of initial conditions and more accurate results are given for the p-system case.
- Differential Geometry
- .......... Page(s) .......... 321
- We prove that on a closed C-manifold cyclic homology of the algebras of (complete) symbols, smoothing and pseudodifferential operators ( DOs) are related by the short exact sequence (symbols) (smoothing operators) and a similar short exact sequence holds in Hochschild homology. Since homology of symbols has been determined before (in [4]) and the algebra of smoothing operators on a closed manifold has the same homology as C, we obtain a complete description of both cyclic and Hochschild homology for the algebra of pseudodifferential operators. Its relation to homology of differential operators is also determined (the answer depends on the Euler characteristic of a manifold).
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- MATHEMATIQUE 1988 - Tome 306 - Série I - n° 6
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