Théorie de Kasparov équivariante et groupo?des I

Let be a locally compact topological groupoid, A and B two C*-algebras endowed with a continuous action of . We define an operator K-theory group K K (A,B). We describe two basic properties of this theory: the existence of a Kasparov product and functoriality with respect to groupoid cocycles.     

On a two-point boundary value problem of duffing type equation with dirichlet conditions

An existence and uniqueness result concerned with the Diriehlet boundary value prob-lem u“ cu‘ g(t,u)=e(t),u(0)=u(π)=0 is offered.     

Implicitly defined harmonic PHH submersions

The concept of harmonic pseudo-horizontally homothetic submersion, alias harmonic PHH submersion, expresses the more geometric notion of smooth family of minimal submanifolds indexed by a K?hler parameter manifold. We give results that allow to construct harmonic PHH submersions by solving some implicit equations and we apply this method to the case of sphere bundles. Received: 3 September 1998 / Accepted: 19 March 1999     

Trialitarian groups and the Hasse principle

Let F be a field of characteristic ≠ 2 such that is of cohomological 2- and 3-dimension ≤ 2. For G a simply connected group of type ³ D ₄ or ⁶ D ₄ over F, we show that the natural map

Generic convergence of infinite products of positive linear operators

We present several results concerning the asymptotic behavior of (random) infinite products of generic sequences of positive linear operators on an ordered Banach space. In addition to a weak ergodic theorem we also obtain convergence to an operator of the formf(·) wheref is a continuous linear functional and is a common fixed point.     

Redheffer's theorem revisited

Based on the Ben Artzi-Gohberg result concerning the equivalence between the invertibility of theL ²-operator and the exponential dichotomic evolution defined byA(t), the time-varying counterpart of the Redheffer theorem is considered under relaxed conditions.     

Gauge symmetries and percolation in ±J Ising spin glasses

We consider the ±J spin glass on a finite graph G=(V,E), with i.i.d. couplings. Our approach considers the Z ₂ local gauge invariance of the system. We see the gauge group as a graph theoretic linear code ? over GF(2). The gauge is fixed by choosing a convenient linear supplement of ?. Assuming some relation between the disorder parameter p and the inverse temperature of the thermal bath β _pb , we study percolation in the random interaction random cluster model, and extend the results to dilute spin glasses. Received: 5 May 1997 / Revised version: 9 April 1998     

K1 of Twisted Rings of Polynomials

We prove that for an arbitrary endomorphism of a ring R the group K1(R[t]) splits into the direct sum of K1(R) and Ñil (r;). Moreover, for any such R and Ñil (R; ) is isomorphic to Ñil (R ; ) for some ring R with : R R – an isomorphism.     

Cyclic Cohomology of étale Groupoids: The General Case

We give a general method for computing the cyclic cohomology of crossed products by étale groupoids, extending the Feigin–Tsygan–Nistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor, and Tsygan for the convolution algebra C _c (G) of an étale groupoid, removing the Hausdorffness condition and including the computation of hyperbolic components. Examples like group actions on manifolds and foliations are considered.     

On the stability of wavelet and Gabor frames (Riesz bases)

If the sequence of functions _{j, k} is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system _j,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of or is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].