Paley-Wiener theorems for a p-Adic spherical variety / Patrick Delorme, Pascale Harinck, Yiannis Sakellaridis.
| Author/creator | Delorme, Patrick |
| Other author | Harinck, Pascale. |
| Other author | Sakellaridis, Yiannis. |
| Format | Electronic |
| Publication Info | Providence. RI : American Mathematical Society, [2021] |
| Description | pages cm. |
| Supplemental Content | Full text available from Memoirs of the American Mathematical Society |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; number 1312 |
| Contents | Boundary degenerations, exponents, Schwartz and Harish-Chandra Schwartz spaces -- Bundles over tori -- Coinvariants and the bundles of X-discrete and X-cuspidal representations -- Discrete summand of the Harish-Chandra Schwartz space -- Cuspidal part of the Schwartz space -- Smooth and unitary asymptotics -- Definition and regularity of Eisenstein integrals -- Goals -- Eigenspace decomposition of Eisenstein integrals -- Scattering : the unitary case -- Scattering : the smooth case -- The Harish-Chandra Schwartz space -- The Schwartz space -- Examples of scattering operators -- The Bernstein center and the group Paley-Wiener theorem. |
| Abstract | "Let SpXq be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let CpXq be the space of Harish- Chandra Schwartz functions. Under assumptions on the spherical variety, which are satisfied when it is symmetric, we prove Paley-Wiener theorems for the two spaces, characterizing them in terms of their spectral transforms. As a corollary, we get relative analogs of the smooth and tempered Bernstein centers - rings of multipliers for SpXq and C pXq. When X " a reductive group, our theorem for CpXq specializes to the well-known theorem of Harish-Chandra, and our theorem for SpXq corresponds to a first step - enough to recover the structure of the Bernstein center - towards the well-known theorems of Bernstein [Ber] and Heiermann [Hei01]"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2021016993 |
| ISBN | 9781470444020 (paperback) |
| ISBN | (pdf) |