Abstract
Given a Müntz–Szàsz sequence of positive real numbers \((\lambda _k)_k\) and a bounded interval \(I\subset {\mathbb {R}}\), Müntz–Szàsz theorem for completeness of the monomials \(\{x^{\lambda _k}\}_k\) in \(L^2(I)\) can be extended to a class of compact extensions of Heisenberg groups. The idea is to define infinitely many coordinate functions of generic unitary representations which are shown to be compactly supported and whose Fourier transforms extend analytically on the complex plane with suitable exponential domination. The representation theory and a Plancherel formula of reducible generic representations play an important role in the proofs.
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The authors are deeply thankful to the referee for the careful reading of the first version of this article. The valuable suggestions have been followed in revising the manuscript.
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Communicating Editor: Parameswaran Sankaran
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Baklouti, A., Ayed, S.B. Müntz–Szàsz analogues for compact extensions of Heisenberg groups. Proc Math Sci 131, 27 (2021). https://doi.org/10.1007/s12044-021-00617-8
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DOI: https://doi.org/10.1007/s12044-021-00617-8