  Discrete solitons of the discrete nonlinear Schr\"odinger (dNLS) equation
become compactly supported in the anti-continuum limit of the zero coupling
between lattice sites. Eigenvalues of the linearization of the dNLS equation at
the discrete soliton determine its spectral and linearized stability. All
unstable eigenvalues of the discrete solitons near the anti-continuum limit
were characterized earlier for this model. Here we analyze the resolvent
operator and prove that it is uniformly bounded in the neighborhood of the
continuous spectrum if the discrete soliton is simply connected in the
anti-continuum limit. This result rules out existence of internal modes
(neutrally stable eigenvalues of the discrete spectrum) of such discrete
solitons near the anti-continuum limit.
