On particle acceleration in turbulent shear boundary layers of relativistic jets

We discuss processes accelerating cosmic ray electrons at boundaries of relativistic jets. The resulting spectrum is expected to posses two characteristic components: a power-law distribution at lower energies and a harder high energy component preceding the high energy cut-off. An example of high energy spectrum from such electron distribution is presented, including the synchrotron and the inverse-Compton components. A characteristic feature of the synchrotron spectrum of such electrons is its highest frequency part which occurs above the power-law fitted to the low frequency spectral range.