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Paley-Wiener theorems for a p-Adic spherical variety / Patrick Delorme, Pascale Harinck, Yiannis Sakellaridis

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 269, number 1312 (January 2021)Publisher: Providence. RI : American Mathematical Society, [2021]Description: v, 102 Seiten : IllustrationenISBN:
  • 9781470444020
Subject(s): Additional physical formats: 9781470464622. | Erscheint auch als: Paley-Wiener theorems for a p-Adic spherical variety. Online-Ausgabe Providence. RI : American Mathematical Society, 2021. 1 Online-Ressource (v, 102 Seiten)MSC: MSC: 22E35 | 43A85RVK: RVK: SI 130LOC classification:
  • QA406
DOI: DOI: 10.1090/memo/1312Summary: 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.Summary: "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]"--PPN: PPN: 1758724137
Holdings
Item type Home library Call number Status
Institutsbestand Fachbibliothek Mathematik Z 57 c Not for loan
Total holds: 0
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