Boundary Conditions via the Cauchy Data

Abstract

To construct all solutions to the problem (7.1), (7.2) by formula (8.5), we need to calculate all “extended Cauchy data ” $v_l^\beta \in S^{\prime }(\overline {{\mathbb R}^+})$, i.e., four functions of one variable. This is the main goal of our approach.Thus, we need at least four equations. Two of the equations follow from the boundary conditions (7.2). The third equation will be extracted from the identity (8.4). The needed additional equation we will obtain by the Malyshev method of automorphic functions .