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- CONTENTS 1985 - VOLUME 300 - SECTION I - N°17
- .......... Page(s) .......... 593
- .......... Page(s) .......... 593
- In this Note we expose a result concerning the asymptotic behaviour of the spectral function for Schrödinger operators Ah=-(h2/2)+V where h0. This asymptotic changes the form on the energy level V(x)=.
- .......... Page(s) .......... 597
- We study propagation and interaction of singularities of the solution of Cauchy problem for strictly hyperbolic semi-linear equations knowing the singularities of the Cauchy datas, extending the results of Rauch and Reed on systems of first order.
- .......... Page(s) .......... 601
- .......... Page(s) .......... 601
- Let be a finitely generated group. We define the space Hof rapidly decreasing functions onand the subspace C of smooth functions on its dual (which is the space of smooth functions on the torus when . We show that the closure of C under holomorphic functional calculus is contained in C, that Cof polynomial growth or free non abelian, but that Cwhen is amenable and not of polynomial growth. We show finally that H is contained inl1 if and anly if is of polynomial growth.
- .......... Page(s) .......... 605
- .......... Page(s) .......... 605
- For a compact Lie group G operating on a C-manifold X, we define a de Rham cohomology H* (G, X), indexed by Z/2Z and a Chern character ch:, where is equivariant K-theory as defined by Atiyah and Segal. We prove that this Chern character induces an isomorphism of K*G with H*(G, X). In the present Note, we assume that G is abelian.
- .......... Page(s) .......... 609
- .......... Page(s) .......... 609
- Let X be the symbolic space IG, where G is a group and I a finite set. We construct a family of invariant ergodic probability measures for the action of G on X by translations. With respect to the vague topology, this family is dense in the convex and compact set M(X, T) of all invariant probabilities if and only if the group is amenable.
- .......... Page(s) .......... 613
- Necessary and sufficient conditions for a random variable with values in a uniformly convex Banach space to satisfy the law of the iterated logarithm are presented. These conditions involve moment hypotheses and a tightness property of the partial sums.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES MATHEMATIQUE 1985 - Tome 300 - Série I - n°17
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