A distribution space for Hilbert transform and its applications
The author introduces a new space \({\mathcal D}_H\) of test functions for the Hilbert transform as the direct sum of \(\mathcal D\) and \(H({\mathcal D})\), and he shows that the Hilbert transform is naturally extended to the dual space \({\mathcal D}_H'\) by conjugation. Here, \({\mathcal D}\) is the space of infinitely differentiable functions with compact support. Also, some characterizations of the space \({\mathcal D}_H\) are given and some nonlinear phase signals are shown to belong to the space \({\mathcal D}'_H\).
scientific article; zbMATH DE number 5643373
scientific article