Characterization of wave front sets by wavelet transforms (Q875706)

To consider wave front sets of tempered distributions, the authors place emphasis on Moritoh's wavelet transforms. In the first part of the paper, they elaborate the wavelet transform \(W_\psi\) and the wave front sets for the wavelet \(\psi\), but for dimensions \(n= 1,2,3,4\) or \(8\), improving some known results concerning the estimates of wave fronts. In Theorem 7, they prove: Let \(f\in S'(\mathbb{R}^n)\). Then \(WF_\psi(f)= WF(f)\), \(n= 1,2,3,4\) or \(8\), where \(WF\) is the wave front defined by Hörmander. In the second part, the authors generalize the definition of \(W_\psi\) transform and extend their results to dimensions \(n\in\mathbb{N}\), excluding some directions in the frequency domain.