|
Matematicheskie Zametki, 2015, Volume 98, Issue 3, paper published in the English version journal
(Mi mzm10932)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Papers published in the English version of the journal
Variants of Müntz–Szàsz Analogs for Euclidean Spin Groups
Salma Azaouzi, Ali Baklouti, Sabria Ben Ayed Sfax University, Sfax, Tunisia
Abstract:
Given a strictly increasing sequence of positive integers $(n_k)_k$, the Müntz–Szàsz theorem for completeness of the monomials $\{x^{n_k}\}$ in $L^2([0,1])$ can be extended to Euclidean spin groups which are the universal coverings of Euclidean motion groups $SO(n) \ltimes \mathbb{R}^n$. Towards such an objective, we rephrase the completeness condition in terms of an integral against the monomials $\{x^{n_k}\}$ of the coordinates functions associated to the Garding vectors of $G$, whose Fourier transform are shown to admit an analytic continuation to the whole complex plane with an exponential domination. This allows us to formulate and prove several variants of Müntz–Szàsz's theorem in these settings. These upshots are proved using the Plancherel theory related to the group Fourier transform.
Keywords:
Müntz–Szàsz theorem, Fourier transform, Plancherel formula, Euclidean motion group, Spin group.
Received: 23.03.2015
Linking options:
https://www.mathnet.ru/eng/mzm10932
|
Statistics & downloads: |
Abstract page: | 11 |
|