  A general theory of edge spin wave excitations in semi-infinite and finite
periodic arrays of magnetic nanodots existing in a spatially uniform
magnetization ground state is developed. The theory is formulated using a
formalism of multi-vectors of magnetization dynamics, which allows one to study
edge excitations in arrays having arbitrary complex primitive cells and lattice
geometry. The developed formalism can describe edge excitations localized both
at the physical edges of the array and at the internal "domain walls"
separating array regions existing in different static magnetization states.
Using a perturbation theory in the framework of the developed formalism it is
possible to calculate damping of edge modes and their excitation by external
variable magnetic fields. The theory is illustrated on the following
practically important examples: (i) calculation of the FMR absorption in a
finite nanodot array having the shape of a right triangle, (ii) calculation of
nonreciprocal spin wave spectra of edge modes, including modes at the physical
edges of an array and modes at the domain walls inside an array, (iii) study of
the influence of the domain wall modes on the FMR spectrum of an array existing
in a non-ideal chessboard antiferromagnetic ground state.
