We construct a family of frames describing the norm and seminorm of the space $H^s(\R^d)$. We also characterise Besov spaces modeled on $L^2(\R^d)$. Our work is inspired by the Discrete Orthonormal Stockwell Transform introduced by R.G. Stockwell, which provides a time-frequency localised version of the Fourier basis of $L^2([0,1])$. This approach is a hybrid between Gabor and Wavelet frames. We construct explicit and computable examples of these frames, discussing their properties and comparing them with the existing literature.
Stockwell-like frames for Sobolev spaces / Battisti, Ubertino; Berra, Michele; Tabacco, Anita Maria. - In: JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. - ISSN 1662-9981. - STAMPA. - 9:4(2018), pp. 701-734.
Titolo: | Stockwell-like frames for Sobolev spaces |
Autori: | |
Data di pubblicazione: | 2018 |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s11868-018-0259-7 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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battisti-berra-tabacco.pdf | Post-print | 2. Post-print / Author's Accepted Manuscript | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2715261