26,737 research outputs found

    Object Reduction in Aleut

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    Remedies Available to the Government Under the Sherman Act

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    The Rate-Making Process

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    Interpolation in Wavelet Spaces and the HRT-Conjecture

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    We investigate the wavelet spaces Wg(Hπ)L2(G)\mathcal{W}_{g}(\mathcal{H}_{\pi})\subset L^{2}(G) arising from square integrable representations π:GU(Hπ)\pi:G \to \mathcal{U}(\mathcal{H}_{\pi}) of a locally compact group GG. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong conditions. Moreover, we use this to derive consequences for wavelet transforms related to convexity and functions of positive type. Motivated by the reproducing kernel Hilbert space structure of wavelet spaces we examine an interpolation problem. In the setting of time-frequency analysis, this problem turns out to be equivalent to the HRT-Conjecture. Finally, we consider the problem of whether all the wavelet spaces Wg(Hπ)\mathcal{W}_{g}(\mathcal{H}_{\pi}) of a locally compact group GG collectively exhaust the ambient space L2(G)L^{2}(G). We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.Comment: Added a relevant citation and made minor modifications to the expositio

    Cartels as Barriers to International Trade

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