Fractional wavelet frames in \(L^{2}(\mathbb{R})\) (Q1799745)

The fractional Fourier transform is a generalization of the classical Fourier transform. Similar to the Fourier transform, it does not give information about the time localization of the spectral components of the analyzed signal. As a remedy for this drawback a fractional wavelet transform had been introduced. The authors of the paper study some properties of this FrWT, namely a possibility of constructing fractional wavelet frames on the real line. They establish a necessary condition and four sufficient conditions for a fractional wavelet system \(\{\psi_{j,k}^\theta: j,k\in\mathbb Z\}\) to be a frame for \(L^2(\mathbb R)\). The results are new and interesting. The proofs are technical and written in a way that makes them difficult to understand. Some preliminary material is missing, especially, a definition of the fractional Fourier transform. Language sloppiness disturbs the reading.