Interpolation in wavelet spaces and the HRT-conjecture
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3024044Utgivelsesdato
2021Metadata
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- Institutt for matematiske fag [2351]
- Publikasjoner fra CRIStin - NTNU [37215]
Originalversjon
Journal of Pseudo-Differential Operators and Applications. 2021, 12 (1), 1-26. 10.1007/s11868-021-00386-ySammendrag
We investigate the wavelet spaces Wg(Hπ)⊂L2(G) arising from square integrable representations π:G→U(Hπ) 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 Wg(Hπ) of a locally compact group G collectively exhaust the ambient space L2(G). We show that the answer is affirmative for compact groups, while negative for the reduced Heisenberg group.