“Quantum trajectories” are solutions of stochastic differential equations also called Belavkin or Stochastic Schrödinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually considered, one is driven by a one-dimensional Brownian motion and the other is driven by a counting process. In this article, we present a way to obtain more adva...

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

The celebrated Trotter approximation theorem provides a sufficient condition for the convergence of sequence operator semigroups in terms corresponding infinitesimal generators. There exist few results on rate Trotter's under some constraints. In present paper, new full generality is given. Moreover, we see that this works well to obtain quantitative estimates limit theorems probability theory.

Lusztig’s presentation of the graded Hecke algebra in terms of generators and relations allows for the definition of algebras associated to noncrystallographic root systems. The representation theory of general graded Hecke algebras is investigated, the expected number of tempered representations for H(H3) are accounted for, and it is shown that one of these representations has the unexpected p...

The above theorems are valid for a representation of a Lie group also. In this case, it is shown that it is possible to extend the representation to elliptic elements of the universal enveloping algebra. It is also shown that the representatives of the strongly elliptic elements of the universal enveloping algebra are the infinitesimal generators of holomorphic semi-groups. Integral representat...