"The metaplectic action on modulation spaces"Shafkulovska, IrinaWe study the mapping properties of metaplectic operators $\widehat{S}\in \mathrm{Mp}(2d,\mathbb{R})$ on modulation spaces of the type $\mathrm{M}^{p,q}_m(\mathbb{R}^d)$. Our main result is a full characterisation of the pairs $(\widehat{S},\mathrm{M}^{p,q}{}(\mathbb{R}^d))$ for which the operator $\widehat{S}:\mathrm{M}^{p,q}{}(\mathbb{R}^d) \rightarrow \mathrm{M}^{p,q}{}(\mathbb{R}^d)$ is (i) well-defined, (ii) bounded. It turns out that these two properties are equivalent, and they entail that $\widehat{S}$ is a Banach space automorphism. Under mild conditions on the weight function, we provide a simple test to determine whether the well-definedness (boundedness) of $\widehat{S}:\mathrm{M}^{p,q}{}(\mathbb{R}^d)\rightarrow \mathrm{M}^{p,q}(\mathbb{R}^d)$ transfers to $\widehat{S}:\mathrm{M}^{p,q}_m(\mathbb{R}^d)\rightarrow \mathrm{M}^{p,q}_m(\mathbb{R}^d)$. |
| https://ps-mathematik.univie.ac.at/e/talks/ICCHA2022_Shafkulovska_2022-07_ICCHA2022_Shafkulovska_The_metaplectic_action_on_modulation_spaces.pdf |
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