In this work, the polygarmonious functions of the nth order satisfying the condition given in some unlimited set of m-dimensional space are considered, having received an integral representation with the help of it, fragmen-Lindelof theorems are obtained and the solution of the regularization problem is considered.

Annotation

In this work, some properties and regulation of the Carlemann function are studied to determine the integral formula of n-th order polygarmonic functions (D ^ n u (y) = 0) and their properties that satisfy the condition 2n≥m in certain unbounded areas of real m-dimensional Euclidean space.

                                                                  Resume

          In this article we consider Carlеman’s functions, to find   integral representation for the polygarmonious functions (Δ^n u(y)=0)defined in unbounded domain of  Euclidean space which  satisfies 2n≥m.

Having obtained an integral representation with the help of it, we obtain theorems of the Phragmen – Lindelöf type.