Searcharxiv⌕ Search

arXiv subjects

Mohamed Vall Ould Moustapha

Publications and source records attributed to Mohamed Vall Ould Moustapha.

13 recordsLinked to original sources
arXiv2026

Poisson semigroup and the Gruet formula for the heat kernels on spaces of constant curvature

This paper is concerned with the Poisson and heat equations on spaces of constant curvature. More explicitly we provide new methods for obtaining old and new explicit formulas for the Poisson and heat semigroups on the Euclidean, spherical and hyperbolic spaces $\R^n$, $§^n$ and $\H^n$ . We obtain the Gruet formula for the heat kernels in Euclidean and spherical spaces $\R^n$ and $§^n$, which are new and we provide a new elementary method to derive the classical Gruet formula Gruet\cite{Gruet} for the kernel of the heat semigroup on the hyperbolic space $\H^n$.

math.AP↗
arXiv2020

Integral Formulas and asymptotic behavior of lattice points in complex hyperbolic space

This paper deals with the $Γ$-lattice points problem associated to a discrete subgroup of motions $Γ$ in the complex hyperbolic space $\mathbb{C} H^n$. We give two integral formulas for the local average of the number $N(T, z, z')$ of $Γ$- lattice points in a sphere of radius $T$ in $\mathbb{C} H^n$. The first on is in terms of the solution of the $Γ$-automorphic wave equation on $\mathbb{C} H^n$ and the second is given in terms of the spectral function of the Laplace-Beltrami operator under $Γ$-automorphic boundary conditions. We use the obtained integral formulas to obtain an asymptotic behavior of the number $N(T, z, z')$ as $T\rightarrow \infty$, with an estimate of the remainder term. Our principal tools are the explicit solution of the wave equation on the complex hyperbolic space, special functions and spectral theory of the Laplace-Beltrami operator under $Γ$ automorphic boundary conditions.

math.CA↗
arXiv2019

Multipliers with inverse square potential and applications I

In this work we give explicit formulas for the Schwartz integral kernels of some multipliers of the Schrödinger operator with inverse square potential on $\R^\ast_+$. By using the integral transforms connecting these multipliers we obtain old and new formulas involving Bessel and hypergeometric functions

math-ph↗
arXiv2019

Wave kernels with magnetic field on the hyperbolic plane and with the Morse potential on the real line

In this article we give explicit solutions for the wave equations associated to the modified Schrödinger operators with magnetic field on the disc and the upper half plane models of the hyperbolic plane. We show that the modified Schrödinger operator with magnetic field on the upper half plane model and the Schrödinger operator with diatomic molecular Morse potential on $\R$ are related by means of one-dimensional Fourier transform. Using this relation we give the explicit forms of the wave kernels associated to the Schrödinger operator with the diatomic molecular Morse potential on $\R$ in terms of the two variables confluent hypergeometric function $Φ_1$.

math-ph↗
arXiv2011

Problème de Cauchy avec des conditions modifiées pour les équations d'Euler-Poisson-Darboux

Nowadays the Euler-Poisson-Darboux equation is extensively studied in several settings. The main questions on avery spaces are explicit solutions for the classical Cauchy problems with the second data null. In this note we will generalize and unify several results on Euler-Poisson-Darboux equation. In this note we consider the Cauchy problem with modified conditions for the Euler-Poisson-Darboux equation. We give the explicit solutions in terms of Gauss 2F1 and Appel F4 hypergeometric functions with applications to the classical and radial wave equations

math-ph↗