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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.03952 |
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| _version_ | 1866908811335303168 |
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| author | Portal, Pierre |
| author_facet | Portal, Pierre |
| contents | We survey the construction of a range of function spaces used in harmonic analysis of PDE, including classical results as well as recent developments. We frame these constructions in a common conceptual framework, where these function spaces arise as retracts of simple function spaces over phase space, through a projection associated with a wave packet decomposition. Finding appropriate function spaces to study a given PDE then consists in choosing a relevant wave packet decomposition. We provide a user guide to making such choices, and constructing the corresponding function spaces. This is done mostly by surveying recent constructions, but we also include a new construction, adapted to Schrödinger operators of the form $Δ- V$ for $V \geq 0$, as a sneak peek into upcoming joint work with Dorothee Frey, Andrew Morris, and Adam Sikora. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Using wave packet decompositions to construct function spaces: a user guide Portal, Pierre Analysis of PDEs Functional Analysis 42B25, 42B37 We survey the construction of a range of function spaces used in harmonic analysis of PDE, including classical results as well as recent developments. We frame these constructions in a common conceptual framework, where these function spaces arise as retracts of simple function spaces over phase space, through a projection associated with a wave packet decomposition. Finding appropriate function spaces to study a given PDE then consists in choosing a relevant wave packet decomposition. We provide a user guide to making such choices, and constructing the corresponding function spaces. This is done mostly by surveying recent constructions, but we also include a new construction, adapted to Schrödinger operators of the form $Δ- V$ for $V \geq 0$, as a sneak peek into upcoming joint work with Dorothee Frey, Andrew Morris, and Adam Sikora. |
| title | Using wave packet decompositions to construct function spaces: a user guide |
| topic | Analysis of PDEs Functional Analysis 42B25, 42B37 |
| url | https://arxiv.org/abs/2602.03952 |