hrt conjecture
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Author(s):  
Eirik Berge

AbstractWe investigate the wavelet spaces $$\mathcal {W}_{g}(\mathcal {H}_{\pi })\subset L^{2}(G)$$ W g ( H π ) ⊂ L 2 ( G ) arising from square integrable representations $$\pi :G \rightarrow \mathcal {U}(\mathcal {H}_{\pi })$$ π : G → U ( H π ) of a locally compact group G. We show that the wavelet spaces are rigid in the sense that non-trivial intersection between them imposes strong restrictions. 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 $$\mathcal {W}_{g}(\mathcal {H}_{\pi })$$ W g ( H π ) of a locally compact group G collectively exhaust the ambient space $$L^{2}(G)$$ L 2 ( G ) . We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.



2020 ◽  
Vol 63 (4) ◽  
pp. 871-881
Author(s):  
B. Currey ◽  
V. Oussa

AbstractWe prove that the HRT (Heil, Ramanathan, and Topiwala) Conjecture is equivalent to the conjecture that co-central translates of square-integrable functions on the Heisenberg group are linearly independent.



2019 ◽  
Vol 25 (4) ◽  
pp. 1874-1901 ◽  
Author(s):  
Kasso A. Okoudjou
Keyword(s):  




2012 ◽  
Vol 388 (1) ◽  
pp. 151-159 ◽  
Author(s):  
Ciprian Demeter ◽  
Alexandru Zaharescu
Keyword(s):  


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