Plancherel and Poisson summation formulae for a family of affine Ψ-bundles
Jayce R. Getz, Miao Pam Gu, Chun-Hsien Hsu
Abstract
We prove a Plancherel formula for a family of affine Ψ-bundles. As an application, we construct Fourier transforms and asymptotic Schwartz spaces for the family. We then prove the corresponding Poisson summation formula under suitable assumptions. The choice of affine Ψ-bundles we consider is motivated by applications to triple product L-functions explored in another paper of the authors and Leslie.
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