The ($n+1$)-Lipschitz homotopy group of the Heisenberg group $\mathbb {H}^n$

The Fourier Transforms of Lipschitz Functions on the Heisenberg Group

We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the Heisenberg group Hn. We compare our conclusions with some previous results in the field.

LIPSCHITZ ESTIMATES FOR GEODESICS IN THE HEISENBERG GROUP by

Volume Preserving Bi-lipschitz Homeomorphisms on the Heisenberg Group

The use of sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on R lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this m...

Smooth Approximation for Intrinsic Lipschitz Functions in the Heisenberg Group

We characterize intrinsic Lipschitz functions as maps which can be approximated by a sequence of smooth maps, with pointwise convergent intrinsic gradient. We also provide an estimate of the Lipschitz constant of an intrinsic Lipschitz function in terms of the L∞−norm of its intrinsic gradient.

The Heisenberg Group Fourier Transform

1. Fourier transform on Rn 1 2. Fourier analysis on the Heisenberg group 2 2.1. Representations of the Heisenberg group 2 2.2. Group Fourier transform 3 2.3. Convolution and twisted convolution 5 3. Hermite and Laguerre functions 6 3.1. Hermite polynomials 6 3.2. Laguerre polynomials 9 3.3. Special Hermite functions 9 4. Group Fourier transform of radial functions on the Heisenberg group 12 Ref...