Unbounded quadrature domains inR n (n≥3)

As a result of the powerful tools of complex analysis a lot of problems have been solved in the theory of Q.D.s (quadrature domain) inR ². These problems are almost untouched inR ⁿ (n≥3). To study Q.D.s inR ⁿ , one has to supply the subject with new techniques. This is the goal of papers by Shapiro, Khavinson and Shapiro, Sakai, and Gustafsson, where the authors approach the subject inR ⁿ by different methods. The main purpose of this paper is to generalize some of the ideas (already known inR ²) toR ⁿ (n>-3), and we merely work with unbounded Q.D.