Green function on the q-symmetric space SUq(2)/U(1)

Invariant distance on the non-commutative C*-algebra C(SUq(2)) is constructed and the generalized functions on the q-symmetric space M = SUq(2)/U(1) are introduced. The Green function and the kernel on M are derived. A path integration is formulated. The Green function for the free massive scalar field on the non-commutative Einstein space R-1 x M is presented.