  We theoretically study the transition radiation of bulk and surface
electromagnetic waves by an electron crossing an interface between a layered
superconductor and an isotropic dielectric. We assume that the direction of the
electron motion and the orientation of the superconducting layers are
perpendicular to the interface. We derive the analytical expressions for the
strongly anisotropic radiation fields and for the time-integrated energy fluxes
of bulk and oblique surface electromagnetic waves (OSWs). We show that the OSWs
with frequencies close to the Josephson plasma frequency $\omega_J$ provide the
main contribution to the OSWs energy flux. Moreover, for frequencies close to
the Josephson plasma frequency, the spectral density of the OSWs radiation
diverges at some critical value of the azimuth angle $\varphi$. At the angles
$\varphi=0$ and $\varphi=90^o$, the radiation field has a transverse magnetic
polarization. We have also studied the Cherenkov radiation by the electron
escaping from the layered superconductor and show that this radiation is almost
monochromatic. A remarkable feature of the Cherenkov radiation in a layered
superconductor is that, contrary to the isotropic case, the Cherenkov radiation
distinctly manifests itself in the angular dependence of the radiation energy
flux.
