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EnglishThis note contains a new characterization of modulation spaces M^p(R^n), 1leq pleq infty, by symplectic rotations. Precisely, instead to measure the time-frequency content of a function by using translations and modulations of a fixed window as building blocks, we use translations and metaplectic operators corresponding to symplectic rotations. Technically, this amounts to replace, in the computation of the M^p(R^n)-norm, the integral in the time-frequency plane with an integral on R^n imes U(2n,R) with respect to a suitable measure, U(2n,R) being the group of symplectic rotations. More conceptually, we are considering a sort of polar coordinates in the time-frequency plane. In this new framework, the Gaussian invariance under symplectic rotations yields to choose Gaussians as suitable window functions. We also provide a similar characterization with the group U(2n,R) being reduced to the n-dimensional torus T^n.
A characterization of modulation spaces by symplectic rotations / Cordero, Elena; De Gosson, Maurice; Nicola, Fabio. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 278:11(2020). [10.1016/j.jfa.2020.108474]
| Titolo: | A characterization of modulation spaces by symplectic rotations | |
| Autori: | ||
| Data di pubblicazione: | 2020 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jfa.2020.108474 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| JFA2020.pdf | post-print editoriale | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
| symplmodspaces-submitted_revised2.pdf | 2. Post-print / Author's Accepted Manuscript |  | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2853971
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