Existence and continuity of solutions to a class of pseudodifferential equations over \(p\)-adic field (Q459989)

Summary: We study the pseudodifferential operator \(T^{\alpha}\) and the pseudodifferential equations of type \(T^{\alpha}u+u=\delta_{x_k}\) over \(p\)-adic field \(\mathbb{Q}_p\), where \(\delta_{x_k}\) is the Dirac delta function. We discuss the existence and uniqueness of solutions to the equations. Furthermore, we give conditions for the continuity of the solutions \(u_k\) when \(u\) belongs to the space \(L^2(\mathbb{Q}_p)\).