This paper is concerned with a data-driven approach for the estimation of infinitesimal generators continuous-time stochastic systems unknown dynamics. We first approximate generator solution process via set data collected from trajectories system. The approximation utilizes both time discretization and sampling process. Assuming proper continuity assumptions on dynamics system, we then quantif...

Infinitesimal holomorphic realizations for the Schrödinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The squeezed states for the unitary irreducible representation of the Jacobi group are introduced. Matrix elements of the squeezed operators, expectation values of polyno...

Remark : An alternative approach, advocated in [4], is to use the infinitesimal invariance criteria, which requires solving a linear system of first order partial differential equations based on the prolonged infinitesimal generators of the transformation group. In contrast, the moving frame method is completely algebraic, typically much simpler, and, moreover provides significantly more inform...

In this paper we provide an easy-to-use characterization of infinitesimal generators of semigroups of holomorphic functions in the polydisk. We also present a number of examples related to that characterization.