"Extension of Anti-Wick operators to ultradistributions with super-exponential kernels"Vučković, ĐorđeIn the Gelfand-Shilov setting, the localisation operator $A^{\varphi_1,\varphi_2}_a$ is equal to the Weyl operator whose symbol is the convolution of $a$ with the Wigner transform of the windows $\varphi_2$ and $\varphi_1$. We employ this fact, to extend the definition of localisation operators to symbols $a$ having very fast super-exponential growth by allowing them to be mappings from $\mathcal D^{\{M_p\}}(\mathbb R^d)$ into $\mathcal D'^{\{M_p\}}(\mathbb R^d)$, where $M_p$, $p\in\mathbb N$, is a non-quasi-analytic Gevrey type sequence. By choosing the windows $\varphi_1$ and $\varphi_2$ appropriately, our main results show that one can consider symbols with growth in position space of the form $\exp(\exp(l|\cdot|^q))$, $l,q>0$. Based on collaborative work with Stevan Pilipovic and Bojan Prangoski. |
| https://ps-mathematik.univie.ac.at/e/talks/strobl22_Vu?kovi?_2022-06_Abstract Djordje Vuckovic.pdf |
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