Plancherel and Poisson summation formulae for a family of affine $\Psi$-bundles

Jayce R. Getz, Miao Pam Gu, Chun-Hsien Hsu

We prove a Plancherel formula for a family of affine $\Psi$-bundles. As an application, we construct Fourier transforms and asymptotic Schwartz spaces for the family. We then prove th…