An \(n\)-dimensional Wiener-Plancherel formula
The authors prove a Wiener-Plancherel formula on \({\mathbb{R}}^ n\). It is an analogue of the Plancherel formula. While the Plancherel formula is valid for finite energy signals, the Wiener-Plancherel formula is valid for signals \(\phi\) having bounded quadratic means. The present formula is based on the local behaviour of the signal on n-dimensional rectangles and the convergence criterion that this geometrical constraint demands.
scientific article; zbMATH DE number 4153165