Related papers: An integral formula on the Heisenberg group

The Mellin transform and several Dirichlet series related with the Riemann zeta function are used to deduce some identities similar to the classical M\"untz formula [4]. These formulas are derived in the critical strip and in the half-plane…

In this article, we prove a series of integral formulae for a codimension-one foliated sub-Riemannian manifold, i.e., a Riemannian manifold $(M,g)$ equipped with a distribution ${\mathcal D}=T{\mathcal F}\oplus\,{\rm span}(N)$, where…

For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such…

We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…

We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of R^d. However, the method used here differs from Rieffel's one: we obtain a Universal…

A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…

We prove an analogue of Chernoff's theorem for the sublaplacian on the Heisenberg group and use it prove a version of Ingham's theorem for the Fourier transform on the same group.

The Heisenberg double $D_q(E_2)$ of the quantum Euclidean group $\mathcal{O}_q(E_2)$ is the smash product of $\mathcal{O}_q(E_2)$ with its Hopf dual $U_q(\mathfrak{e}_2)$. For the algebra $D_q(E_2)$, explicit descriptions of its prime,…

We continue the systematic study of left-invariant generalised Einstein metrics on Lie groups initiated in arXiv:2206.01157. Our approach is based on a new reformulation of the corresponding algebraic system. For a fixed Lie algebra…

We study isometries in the contact sub-pseudo-Riemannian geometry. In particular we give an upper bound on the dimension of the isometry group of a general sub-pseudo-Riemannian manifold and prove that the maximal dimension is attained for…

We derive sufficient conditions under which the ``second'' Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical $\cal W$-algebras obtained through Drinfel'd-Sokolov Hamiltonian reduction. These…

We prove that in the first Heisenberg group, unlike Euclidean spaces and higher dimensional Heisenberg groups, the best possible exponent for the strong geometric lemma for intrinsic Lipschitz graphs is $4$ instead of $2$. Combined with…

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This…

In this paper, we establish Liouville type results for semilinear subelliptic systems associated with the sub-Laplacian on the Heisenberg group $\mathbb{H}^{n}$ involving two different kinds of general nonlinearities. The main technique of…

We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate…

In this paper we generalize an identity first given by Heinrich Eduard Heine in his treatise, {\it Handbuch der Kugelfunctionen, Theorie und Anwendungen (1881), which gives a Fourier series for $1/[z-\cos\psi]^{1/2}$, for $z,\psi\in\R$, and…

Let k>n be positive integers. We consider mappings from a subset of k-dimensional Euclidean space R^k to the Heisenberg group H^n with a variety of metric properties, each of which imply that the mapping in question satisfies some weak form…

We determine all Ricci flat left invariant Lorentzian metrics on simply connected 2-step nilpotent Lie groups. We show that the $2k+1$-dimensional Heisenberg Lie group $H_{2k+1}$ carries a Ricci flat left invariant Lorentzian metric if and…

In 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias obtained an…

Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian $H=\frac 12 p_u^2+\alpha(u)L+\beta(u)$ with new canonically conjugated coordinates…