The theory of pseudodifferential operators and Fourier integral operators on compact manifolds is well established and their applications in mathematical physics well known , see for example Hörmander , Duistermaat , Treves 12 . For open (non compact) manifolds this is not the case, and that’s what I would like to focus on in this paper. We are interested in the geometry of the spaces of pseudo...

We prove that if the group generated by an invertible and reversible Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth for a restricted family of automaton (semi)groups. The purpose of this note is to link up two classes of groups and semigroups high...

We present a way of thinking of exponential families as geodesic surfaces in the class of positive functions considered as a (multiplicative) sub-group G of the group G of all invertible elements in the algebra A of all complex bounded functions defined on a measurable space. For that we have to study a natural geometry on that algebra. The class D of densities with respect to a given measure w...

In this article, only connected bipartite graphs G with a unique perfect matching M are considered. Let Gw denote the weighted graph obtained from G by giving weights to its edges using the positive weight function w : E(G)→ (0,∞) such that w(e) = 1 for each e ∈ M. An unweighted graph G may be viewed as a weighted graph with the weight function w ≡ 1 (all ones vector). A weighted graph Gw is no...

In this paper we compute the second homology of the discrete jet groups. Let R be the additive group of real numbers and R the multiplicative group of positive reals. The n jet group Jn = {rx+a2x + · · ·+anx | r ∈ R, ai ∈ R} is the group, under composition followed by truncation, of invertible, orientationpreserving real n-jets at 0. Consider the homomorphism D : Jn → R obtained by projecting o...