Orthonormal sequences in \(L^{2}(\mathbb{R}^{d})\) and time frequency localization (Q620413)

The main aim of this paper is to give a version of time-frequency localization that yields a number of precise uncertainty inequalities for orthonormal sequences and bases. The approach is simple and works in \(\mathbb{R}^4\) for any \(d\). Here the author considers the operator that first time limits the function and then frequency-limits it. He used an elementary calculation of the trace of the corresponding selfadjoint operator instead of using the theory of prolate spheroidal wave functions and the 2WT approximation theorem.