Solvability theory of the generalized Riemann boundary value problem

Abstract

In the preceding Chapters 2 and 3, we constructed the solvability theory of binomial boundary value problems with shift and complex conjugated limit values. In qualitative aspects this theory has the same character as the solvability theory of Riemann’s boundary value problem for one piecewise analytic function. Only the explicit form of solution is lost in the general case, but the numbers of linearly independent solutions and solvability conditions depend only on the index of the problem and can be calculated. Now we move on to construct the solvability theory for polynomial boundary value problems with shift and complex conjugation. We start with the so-called generalized Riemann boundary value problem.