  Boundary multifractality of electronic wave functions is studied analytically
and numerically for the power-law random banded matrix (PRBM) model, describing
a critical one-dimensional system with long-range hopping. The peculiarity of
the Anderson localization transition in this model is the existence of a line
of fixed points describing the critical system in the bulk. We demonstrate that
the boundary critical theory of the PRBM model is not uniquely determined by
the bulk properties. Instead, the boundary criticality is controlled by an
additional parameter characterizing the hopping amplitudes of particles
reflected by the boundary.
