2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96579Harmonic 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 χ_{NP} of the torus action on H^0(M, L^N).20 pagesComplex VariablesAlgebraic Geometrytext