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- W4299640757 abstract "Let $G$ be a connected, simply connected nilpotent group and $pi$ be a square-integrable irreducible unitary representation modulo its center $Z(G)$ on $L^2(mathbf{R}^d)$. We prove that under reasonably weak conditions on $G$ and $pi$ there exist a discrete subset $Gamma$ of $G/Z(G)$ and some (relatively) compact set $F subseteq mathbf{R}^d$ such that $$bigl { |F|^{-1/2} hspace{2pt} pi(gamma) 1_F mid gamma in Gamma bigr}$$ forms an orthonormal basis of $L^2(mathbf{R}^d)$. This construction generalizes the well-known example of Gabor orthonormal bases in time-frequency analysis. The main theorem covers graded Lie groups with one-dimensional center. In the presence of a rational structure, the set $Gamma $ can be chosen to be a uniform subgroup of $G/Z$." @default.
- W4299640757 created "2022-10-02" @default.
- W4299640757 creator A5001099862 @default.
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- W4299640757 date "2017-06-19" @default.
- W4299640757 modified "2023-10-14" @default.
- W4299640757 title "Orthonormal Bases in the Orbit of Square-Integrable Representations of Nilpotent Lie Groups" @default.
- W4299640757 doi "https://doi.org/10.48550/arxiv.1706.06034" @default.
- W4299640757 hasPublicationYear "2017" @default.
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