  %context {Recent observations of hard X-rays and very high energy gamma-rays
from a number of young shell type supernova remnants indicate the importance of
detailed quantitative studies of energy spectra of relativistic electrons
formed via diffusive shock acceleration accompanied by intense nonthermal
emission through synchrotron radiation and inverse Compton scattering.} %aim
{The aim of this work was derivation of exact asymptotic solutions of the
kinetic equation which describes the energy distribution of shock-accelerated
electrons for an arbitrary energy-dependence of the diffusion coefficient.}
%method {The asymptotic solutions at low and very high energy domains coupled
with numerical calculations in the intermediate energy range allow analytical
presentations of energy spectra of electrons for the entire energy region.}
%results {Under the assumption that the energy losses of electrons are
dominated by synchrotron cooling, we derived the exact asymptotic spectra of
electrons without any restriction on the diffusion coefficient. We also
obtained simple analytical approximations which describe, with accuracy better
than ten percent, the energy spectra of nonthermal emission of
shock-accelerated electrons due to the synchrotron radiation and inverse
Compton scattering.} %conclusions {The results can be applied for
interpretation of X-ray and gamma-ray observations of shell type supernova
remnants, as well as other nonthermal high energy source populations like
microquasars and large scale synchrotron jets of active galactic nuclei.
