A characterization of bi-invariant Schwartz space multipliers on nilpotent Lie groups
A Distribution - Theoretic Proof of Kirillov's Character Formula for Nilpotent Lie Groups.
A functional calculus for Rockland operators on nilpotent Lie groups
A Kirillov theory for divisible nilpotent groups.
A new criterion for local non-solvability of homogeneous left invariant differential operators on nilpotent Lie groups.
A Paley-Wiener theorem for nilpotent Lie groups. (Un théorème de Paley-Wiener pour les groupes de Lie nilpotents.)
A Paley-Wiener theorem on NA harmonic spaces
Let N be an H-type group and consider its one-dimensional solvable extension NA, equipped with a suitable left-invariant Riemannian metric. We prove a Paley-Wiener theorem for nonradial functions on NA supported in a set whose boundary is a horocycle of the form Na, a ∈ A.
A Qualitative Uncertainty Principle for Certain Locally Compact Groups.
A remark on a Marcinkiewicz-Hörmander multiplier theorem for some non-differential convolution operators
A semi-group of probability measures with non-smooth differentiable densities on a Lie group
A smooth subadditive homogeneous norm on a homogeneous group
A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)
Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.
Abelian simply transitive affine groups of symplectic type
The set of all Abelian simply transitive subgroups of the affine group naturally corresponds to the set of real solutions of a system of algebraic equations. We classify all simply transitive subgroups of the symplectic affine group by constructing a model space for the corresponding variety of solutions. Similarly, we classify the complete global model spaces for flat special Kähler manifolds with a constant cubic form.
Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K.T. Chen
Algorithmic orbit classification for some Borel group actions
An analogue of Hardy's theorem for the Heisenberg group
We observe that the classical theorem of Hardy on Fourier transform pairs can be reformulated in terms of the heat kernel associated with the Laplacian on the Euclidean space. This leads to an interesting version of Hardy's theorem for the sublaplacian on the Heisenberg group. We also consider certain Rockland operators on the Heisenberg group and Schrödinger operators on ℝⁿ related to them.
An extension of Mahler's theorem to simply connected nilpotent groups
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
An extention of Nomizu’s Theorem –A user’s guide–
For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ, C) of the solvmanifold Γ. In this note, we give a quick introduction to the construction of such A*Γ including a simple proof of H*(A*Γ) ≅ H*(Γ, C).
Applications of the Theory of Hardy Spaces to Harmonic Analysis on the Heisenberg Groups.
Asymptotic behavior of solutions of Schrödinger inequalities on unbounded domains of nilpotent Lie groups