On a New Method for Solving Irregular Problems

We suggest a new approach to the investigation of boundary value problems with a parameter in the case when the parameter appears in both the equation and the boundary conditions. The method is applied to the Regge problem. In spite of the fact that the Regge problem is Birkhoff-irregular see G. D. Birkhoff, Trans. Amer. Math. Soc. 9, 1908, 373]395., the problem is coercive but with a defect with respect to the spectral parameter. We also prove 2-fold completeness of root functions of the Regge problem