Ramanujan's master theorem for radial sections of line bundle over noncompact symmetric spaces

Abstract

We prove analogues of Ramanujan's Master theorem for the radial sections of the line bundles over the Poincar\'{e} upper half plane $\mathrm{SL}(2, \R)/\mathrm{SO}(2)$ and over the complex hyperbolic spaces $\mathrm {SU}(1, n)/ S(\mathrm{U}(1) \times \mathrm{U}(n))$.