  We consider a dilute gas of bosons with repulsive contact interactions,
described on the mean-field level by the Gross-Pitaevskii equation, and bounded
by an impenetrable "hard" wall (either rigid or flexible). We solve the
Bogoliubov-de Gennes equations for excitations on top of the Bose-Einstein
condensate analytically, by using matrix-valued hypergeometric functions. This
leads to the exact spectrum of gapless Bogoliubov excitations localized near
the boundary. The dispersion relation for the surface excitations represents
for small wavenumbers $k$ a ripplon mode with fractional power law dispersion
for a flexible wall, and a phonon mode (linear dispersion) for a rigid wall.
For both types of excitation we provide, for the first time, the exact
dispersion relations of the dilute quantum liquid for all $k$ along the
surface, extending to $k \rightarrow \infty$. The small wavelength excitations
are shown to be bound to the surface with a maximal binding energy $\Delta=
\frac18 (\sqrt{17}-3)^2 mc^2 \simeq 0.158\, mc^2$, which both types of
excitation asymptotically approach, where $m$ is mass of bosons and $c$ bulk
speed of sound. We demonstrate that this binding energy is close to the
experimental value obtained for surface excitations of helium II confined in
nanopores, reported in Phys. Rev. B 88, 014521 (2013).
