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• W3137093501 abstract "Braverman and Kazhdan proposed a conjecture, later refined by Ngo and broadened to the framework of spherical varieties by Sakellaridis, that asserts that affine spherical varieties admit Schwartz spaces, Fourier transforms, and Poisson summation formulae. The first author in joint work with B.~Liu and later the first two authors proved these conjectures for certain spherical varieties $Y$ built out of triples of quadratic spaces. However, in these works the Fourier transform was only proven to exist. In the present paper we give, for the first time, an explicit formula for the Fourier transform on $Y.$ We also prove that it is unitary in the nonarchimedean case. As preparation for this result, we give explicit formulae for Fourier transforms on Braverman-Kazhdan spaces attached to maximal parabolic subgroups of split, simple, simply connected groups. These Fourier transforms are of independent interest, for example, from the point of view of analytic number theory." @default.
• W3137093501 created "2021-03-29" @default.
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• W3137093501 date "2021-03-18" @default.
• W3137093501 modified "2023-09-27" @default.
• W3137093501 title "Harmonic analysis on certain spherical varieties" @default.
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• W3137093501 hasPublicationYear "2021" @default.
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