Resumen de A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)

David Kazhdan

• Let F be a local non-archimedian field, G a semisimple F-group, dg a Haar measure on G and S(G) be the space of locally constant complex valued functions f on G with compact support. For any regular elliptic congugacy class Ω=hG⊂G we denote by IΩ the G-invariant functional on S(G) given by IΩ(f)=∫Gf(g−1hg)dg This paper provides the spectral decomposition of functionals IΩ in the case G=PGL(2,F) and in the last section first steps of such an analysis for the general case.