An integrated fractional Fourier transform

AbstractFor 0 < α < 2, an integrated fractional Fourier transform Fα of Wiener type, closely related to fractional Levy Brownian motion Xα, is established. By means of this transform, transform, the reproducing Kernel Hilbert space and the covariance operator of Xα are characterized and the connection between Xα and the Laplacian is shown. As a further application a Blaschke-Fuglede-type theorem for a fractional Radon transform is derived