Boundary value problems with shift for generalized analytic vectors

This paper is a survey of the most important work of the well-known Georgian mathematician Professor Giorgi Manjavidze “Boundary value problems for analytic and generalized analytic functions”. Here we present his original approach to the subject. The main attention is paid to the construction of the canonical matrices which are used in the construction of the general solutions of the considered problems. Explicit conditions of normal solvability and index formulas are obtained.