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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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