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Paley-Wiener theorems for a p-Adic spherical variety / Patrick Delorme, Pascale Harinck, Yiannis Sakellaridis.
Math/Physics/Astronomy Library QA3 .A57 no.1312
Available
- Format:
- Book
- Author/Creator:
- Delorme, Patrick, author.
- Harinck, Pascale, author.
- Sakellaridis, Yiannis, author.
- Series:
- Memoirs of the American Mathematical Society ; no. 1312.
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1312
- Language:
- English
- Subjects (All):
- Spherical harmonics.
- p-adic analysis.
- Fourier analysis.
- Schwartz spaces.
- Scattering (Mathematics).
- Smoothness of functions.
- Lie algebras.
- Physical Description:
- v, 102 pages : illustrations ; 26 cm.
- Place of Publication:
- Providence. RI : American Mathematical Society, [2021]
- 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]"-- Provided by publisher.
- 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.
- Notes:
- Includes bibliographical references.
- ISBN:
- 9781470444020
- 147044402X
- OCLC:
- 1228924281
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