  We use renormalization group methods to study composite operators existing at
a boundary of an interacting conformal field theory. In particular we relate
the data on boundary operators to short-distance (near-boundary) divergences of
bulk two-point functions. We further argue that in the presence of running
couplings at the boundary the anomalous dimensions of certain composite
operators can be computed from the relevant beta functions and remark on the
implications for the boundary (pseudo) stress-energy tensor. We apply the
formalism to a scalar field theory in $d=3-\epsilon$ dimensions with a quartic
coupling at the boundary whose beta function we determine to the first
non-trivial order. We study the operators in this theory and compute their
conformal data using $\epsilon-$expansion at the Wilson-Fisher fixed point of
the boundary renormalization group flow. We find that the model possesses a
non-zero boundary stress-energy tensor and displacement operator both with
vanishing anomalous dimensions. The boundary stress tensor decouples at the
fixed point in accordance with Cardy's condition for conformal invariance. We
end the main part of the paper by discussing the possible physical significance
of this fixed point for various values of $\epsilon$.
