Zobrazeno 1 - 10
of 1 181
pro vyhledávání: '"22E30"'
We prove that the uniform doubling property holds for every Lie group which can be written as a quotient group of $\operatorname{SU}(2) \times \mathbb{R}^n$ for some $n$. In particular, this class includes the four-dimensional unitary group $\operato
Externí odkaz:
http://arxiv.org/abs/2412.17102
Autor:
Niedorf, Lars
We prove an $L^p$-spectral multiplier theorem under the sharp regularity condition $s > d\left|1/p - 1/2\right|$ for sub-Laplacians on M\'etivier groups. The proof is based on a restriction type estimate which, at first sight, seems to be suboptimal
Externí odkaz:
http://arxiv.org/abs/2412.07920
We consider a (possibly discrete) unimodular locally compact group $G$ with Haar measure $\mu_G$, and a compact $A\subseteq G$ of positive measure with $\mu_G(A^2)\leq K\mu_G(A)$. Let $H$ be a closed normal subgroup of G and $\pi: G \rightarrow G/H$
Externí odkaz:
http://arxiv.org/abs/2411.17246
Autor:
Gupta, Sanjeev Kumar, Spronk, Nico
For rank 1 flat symmetric spaces, continuous orbital measures admit absolutely continuous convolution squares, except for Cartan type AI. Hence $L^1$-$L^2$ dichotomy for these spaces holds true in parallel to the compact and non-compact rank 1 symmet
Externí odkaz:
http://arxiv.org/abs/2411.15564
Autor:
Dewan, Utsav
In this article, we consider the Schr\"odinger equation corresponding to the Laplace-Beltrami operator with radial initial data on Damek-Ricci spaces and study the Carleson's problem of pointwise convergence of the solution to its initial data along
Externí odkaz:
http://arxiv.org/abs/2411.14020
Autor:
Shehata, Ayman, Kumar, Dinesh
The study is devoted to the construction of dynamical symmetry algebra of confluent hypergeometric function $_1F_1$ and $\Psi_2$-Humbert function and to derive some generating relations and reduction formulas for $_1F_1$ and $\Psi_2$ functions.
Externí odkaz:
http://arxiv.org/abs/2411.08828
Autor:
Dewan, Utsav, Ray, Swagato K.
Let $\Delta$ be the Laplace-Beltrami operator on a Damek-Ricci space $S$ corresponding to the left-invariant Riemannian metric, with its $L^2$-spectrum being the half line $(-\infty, -Q^2/4]$. Then for a radial $L^2$-Schwartz class function $f$, we c
Externí odkaz:
http://arxiv.org/abs/2411.04084
Autor:
Papageorgiou, Effie
The main goal of this work is to study the $L^p$-asymptotic behavior of solutions to the heat equation on arbitrary rank Riemannian symmetric spaces of non-compact type $G/K$ for non-bi-$K$ invariant initial data. For initial data $u_0$ compactly sup
Externí odkaz:
http://arxiv.org/abs/2411.02940
Autor:
Papageorgiou, Effie
Let $\mu$ be a radial compactly supported distribution on a harmonic $NA$ group. We prove that the right convolution operator $c_{\mu}:f \mapsto f* \mu$ maps the space of smooth $\mathfrak{v}$-radial functions onto itself if and only if the spherical
Externí odkaz:
http://arxiv.org/abs/2410.15043
This is a slightly edited translation of a paper in Dutch which appeared in Nieuw Archief voor Wiskunde (5) 25 (2024), No.2, 87-90 on the occasion of I.G. Macdonald's death in 2023, and aimed at a very broad mathematical audience. First we review som
Externí odkaz:
http://arxiv.org/abs/2410.07882