Related papers: Non-Euclidean Fourier inversion on super-hyperboli…
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…
We establish sharp Hardy-Adams inequalities on hyperbolic space $\mathbb{B}^{4}$ of dimension four. Namely, we will show that for any $\alpha>0$ there exists a constant $C_{\alpha}>0$ such that \[ \int_{\mathbb{B}^{4}}(e^{32\pi^{2}…
The p-harmonic functions are preserved under reflections in spheres only if the exponent p > 1 is equal to the dimension of the underlying Euclidean space. In the linear case p = 2 the Kelvin transform corrects this lack of invariance. We…
As an appropriate analog of the Euclidean short-time Fourier transform, we study a windowed version of the Helgason-Fourier transform on the complex unit ball and translate the theory of modulation/coorbit spaces. As a result, atomic…
The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields in one variable over a henselian valued field with…
We investigate the distribution of orbits of a non-elementary discrete hyperbolic group acting on the n-dimensional hyperbolic space and its geometric boundary. In particular, we show that if the group $\Gamma$ admits a finite…
The long-standing problem of transverse Lambda polarization in high-energy collisions of unpolarized hadrons can be tackled by considering new, spin and k_T-dependent quark fragmentation functions for an unpolarized quark into a polarized,…
This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation $c(x)\partial_{t}^{2}u - \Delta u = 0$ in a bounded smooth domain in $\R^{d}$ from partial (on part of the boundary) dynamic…
We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a…
We present a Fourier Continuation-based parallel pseudospectral method for incompressible fluids in cuboid non-periodic domains. The method produces dispersionless and dissipationless derivatives with fast spectral convergence inside the…
Recently the correlation functions of the so-called Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact…
We investigate properties of some spherical fonctions defined on hyperbolic groups using boundary representations on the Gromov boundary endowed with the Patterson-Sullivan measure class. We prove sharp decay estimates for spherical…
Properties of Hamiltonian symmetry flows on hyperbolic Euler-type Liouvillean equations E' are analyzed. Description of their Noether symmetries assigned to the integrals for these equations is obtained. The integrals provide Miura…
Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is…
We continue our research on Fourier restriction for hyperbolic surfaces, by studying local perturbations of the hyperbolic paraboloid $z=xy$ which are of the form $z=xy+h(y),$ where $h(y)$ is a smooth function which is flat at the origin.…
This paper is concerned with the Poisson transform of differential forms on the hyperbolic space $H^n(\mathbb R)$. Consider an integer $p$ such that $1\leqslant p\leqslant n$ and let $q$ be either $p-1$ or $p$. For $1<r<\infty$, we prove…
In this paper, we first prove that the cubic, defocusing nonlinear Schr\"odinger equation on the two dimensional hyperbolic space with radial initial data in $H^s(\mathbb{H}^2)$ is globally well-posed and scatters when $s > \frac{3}{4}$.…
It is a classical theorem that if a function is integrable along the boundary of the unit circle, then the function is the nontangential limit of a holomorphic function on the open disc if and only if its Fourier coefficients for…
We study the neural field equations introduced by Chossat and Faugeras in their article to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure…
The Atiyah-Hitchin manifold is the moduli space of parity inversion symmetric charge two SU(2) monopoles in Euclidean space. Here a hyperbolic analogue is presented, by calculating the boundary metric on the moduli space of parity inversion…