A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic c...

Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standar...

We give a formula for the one-parameter strongly continuous semigroup e−tL, t > 0, generated by the Hermite operator L on the Heisenberg group H1 in terms of Weyl transforms, and use it to obtain an L2 estimate for the solution of the initial value problem for the heat equation governed by L in terms of the Lp norm of the initial data for 1 ≤ p ≤ ∞. This research has been partially supported by...

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfan...

We construct an explicit solution of the Cauchy initial value problem for the onedimensional Schrödinger equation with time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator) is derived with the help of the generalized Fourier transform and a relation with representations of the Heisenberg–Weyl group N (3) in a certain special case a...

In this paper it is shown that a quantum observable algebra, the Heisenberg-Weyl algebra, is just given as the Hopf algebraic dual to the classical observable algebra over classical phase space and the Plank constant is included in this scheme of quantization as a compatible parameter living in the quantum double theory.In this sense,the quantum Yang-Baxter equation naturally appears as a neces...

In this article, we prove that (unit sphere, non-harmonic cone) is a Heisenberg uniqueness pair for the symplectic Fourier transform on C n . We derive spheres as well cones are determining sets spectral projections of finite measure supported unit sphere. Further, if finitely function step two nilpotent Lie group arbitrary rank, then must be zero. The latter result correlates to annihilating W...