  We develop a method for constructing of the basic functions with witch to
expand small perturbations of space-time in General Relativity. The method
allows to obtain the tensor harmonics for perturbations of the background
space-time admitting an arbitrary group of isometry, and to split the
linearized Einstein equations into the irreducible combinations. The essential
point of the work is the construction of the generalized Casimir operator for
the underlying group, which is defined not only on vector but also on tensor
fields. It is used to construct the basic functions for spaces of tensor
representations of the background metric's group of isometry. The method, being
general, is applied here to construction of the basic functions for the case of
the three-parameter group of isometry G_3 acting on the two-dimensional
non-isotropic surface of transitivity. As quick illustrations of the method we
consider the well-known particular cases: cylindrical harmonic for the flat
space-time, and Regge-Wheller spherical harmonics for the Schwarzschild metric.
