A fractional power theory for Hankel transform in \(L^ 2(\mathbb{R}^ +)\) (Q1176163)

The author presents a fractional power theory for the Hankel transform of order \(\nu\) in \(L^ 2(\mathbb{R}^ +)\) for suitably restricted values of \(\nu\). The motivation for the theory lies in the work of \textit{V. Namias} [J. Inst. Math. Appl. 26, 187-197 (1980; 454.44001)]. The author points out that fractionalisations of Fourier Cosine and Fourier Sine transforms are special cases of the fractionalisation of the Hankel transform of order \(\nu\) for \(\nu=-{1/2}\) and \(\nu={1/2}\), respectively.