Subexponential decay and regularity estimates for eigenfunctions of localization operators (Q2066085)

Inspired by the recent work [\textit{D. Bayer} and \textit{K. Gröchenig}, Integral Equations Oper. Theory 82, No. 1, 95--117 (2015; Zbl 1337.47029)], the authors consider the properties of eigenfunctions of compact localization operators. They extend the framework of the Schwartz space of test functions and its dual space of tempered distributions given in the previous reference by replacing it with a more subtle family of Gelfand-Shilov spaces and their duals, spaces of ultra-distributions. As an important technical tool, the authors consider a class of weights which contains the weights of subexponential growth, apart from polynomial type weights. Among the main tools is the \(\tau \)-Wigner distribution \(W_{\tau }(f,g)\) with \(f,g\in L^{2}(\mathbb{R}^{2}).\)