Harmonic Analysis on Toric Varieties
| dc.creator | Shiffman, B. | |
| dc.creator | Tate, T. | |
| dc.creator | Zelditch, S. | |
| dc.date | 2003-03-26 | |
| dc.date.accessioned | 2026-07-07T06:24:33Z | |
| dc.date.available | 2026-07-07T06:24:33Z | |
| dc.description | 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 χ_{NP} of the torus action on H^0(M, L^N). | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0303337 | |
| dc.identifier | http://arxiv.org/abs/math/0303337 | |
| dc.identifier | Explorations in Complex and Riemannian Geometry: A Volume Dedicated to Robert E. Greene, Contemporary Mathematics, vol. 332, Amer. Math. Soc., Providence, RI, 2003, pp. 267-286. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96579 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.title | Harmonic Analysis on Toric Varieties | |
| dc.type | text |