Pseudodifferential Equations and Boundary Value Problems in a Multidimensional Cone

We consider a special boundary value problem in the Sobolev–Slobodetskii space for a model elliptic pseudodifferential equation in a multidimensional cone. Taking into account the special factorization of the elliptic symbol, we write the general solution of the pseudodifferential equation that contains an arbitrary function. To determine it unambiguously, some integral condition is added to the equation, which makes it possible to write the solution in Fourier transforms.