Extremizers for Adjoint Restriction to Pairs of Translated Paraboloids

Consider the adjoint restriction inequality associated with the hypersurface ${ (\tau, \xi) \in $\mathbb{R}$^{d+1} : \tau = |\xi|^2 } \cup {(\tau, \xi) \in $\mathbb{R}$^{d+1} : \tau - \tau_0 = |\xi - \xi_0|^2}$forany$(\tau_0, \xi_0) \neq 0$. We prove that extremizers do not exist for this inequality and fully characterize extremizing sequences in terms of extremizers for the adjoint restriction inequality for the paraboloid.