Time-frequency analysis on the adeles over the rationals
| Autor: | Franz Luef, Ulrik Enstad, Mads Sielemann Jakobsen |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics::Functional Analysis
Rational number Pure mathematics Mathematics::Number Theory 010102 general mathematics Mathematics - Operator Algebras General Medicine 01 natural sciences Time–frequency analysis Functional Analysis (math.FA) Mathematics - Functional Analysis Computer Science::Sound Computer Science::Computer Vision and Pattern Recognition Lattice (order) 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Operator Algebras (math.OA) Mathematics |
| ISSN: | 1631-073X |
| DOI: | 10.48550/arxiv.1807.07011 |
| Popis: | We show that the construction of Gabor frames in $L^{2}(\mathbb{R})$ with generators in $\mathbf{S}_{0}(\mathbb{R})$ and with respect to time-frequency shifts from a rectangular lattice $\alpha\mathbb{Z}\times\beta\mathbb{Z}$ is equivalent to the construction of certain Gabor frames for $L^{2}$ over the adeles over the rationals and the group $\mathbb{R}\times\mathbb{Q}_{p}$. Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on $\mathbb{R}\times\mathbb{Q}_{p}$ with the construction of certain Heisenberg modules. Comment: minor revisions, added more references, added a Balian-Low type result in the form of Proposition 4.4 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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