  We consider a superconductor with surface suppression of the BCS pairing
constant $\lambda(x)$. We analytically find the gap in the surface density of
states (DOS), behavior of the DOS $\nu(E)$ above the gap, a "vertical"
peculiarity of the DOS around an energy equal to the bulk order parameter
$\Delta_0$, and a perturbative correction to the DOS at higher energies. The
surface gap in the DOS is parametrically different from the surface value of
the order parameter due to a difference between the spatial scale $r_c$, at
which $\lambda(x)$ is suppressed, and the coherence length. The vertical
peculiarity implies an infinite-derivative inflection point of the DOS curve at
$E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The
coefficients of this dependence are different at $E<\Delta_0$ and $E>\Delta_0$,
so the peculiarity is asymmetric.

Superconductivity;Mesoscale and Nanoscale Physics