On a summation formula for triples of quadratic spaces

Following conjectures by Braverman-Kazhdan and Sakellaridis, Getz and Liu proved a summation formula for the spherical variety attached to a triple of quadratic forms. In the joint work with Getz, we strengthen the summation formula in two fashions. We prove that the Fourier transform, which was previously known only as a correspondence, defines an isomorphism of the Schwartz space. We additionally allow more general test functions which in turn introduce boundary terms into the formula.