  Harmonic analysis on a toric Kahler variety M refers to the orthonormal basis
of eigenfunctions of the complex torus action on the spaces H^0(M, L^N) of
holomorphic sections of powers of a positive line bundle L and the Fourier
multipliers that act on them. Using this harmonic analysis, we give an exact
formula for the Szego kernel as a Fourier multiplier applied to the pull back
of the Szego kernel of projective space under a monomial embedding. The Fourier
multiplier involves a partition function of the convex lattice polytope P
associated to M. We further prove that this Fourier multiplier is a Toeplitz
operator, and as a corollary we obtain an oscillatory integral formula for the
characters \chi_{NP} of the torus action on H^0(M, L^N).
