TENSOR HARMONIC-ANALYSIS ON HOMOGENEOUS SPACES

The Hilbert space of tensor functions on a homogeneous space with the compact stability group is considered. The functions are decomposed on to a sum of tensor plane waves (defined in the text), components of wh ich are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitut es a unitary transformation, which allows to obtain the Parseval equal ity. The Fourier components call be calculated by means of the Fourier transformation, the form of which is given explicitly.