Journal of the Ramanujan Mathematical Society
Volume 37, Issue 3, September 2022 pp. 287–300.
Müntz-Szász theorem for connected nilpotent Lie groups
Authors:
Ali Baklouti, Mouna Chaabouni and Raza Lahiani
Author institution:Laboratory Applied Mathematics and Harmonic Analysis,
Faculty of Sciences of Sfax, University of Sfax Tunisia, BP 1171, 3000 SFAX, Tunisia
Summary:
We generate and prove in the setting of a connected and a simply connected
nilpotent Lie group, an analogue of Müntz-Szász theorem proved way back in
1914 for L{2}([0,1]). This requires to introduce the notion of real Müntz-Szász
sequences and their generalized powers and allows to establish some analogues
for L{2}{c}(Rn) and C{c}(R{n}),n ∈ N{*}. The rational parametrization of the layer of
generic coadjoint orbits also appears to be a key point to generate such an
analogue.
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