Boundary value problems with shift for generalized analytic vectors

Nino Manjavidze, George Akhalaia

Abstract


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.

Keywords


boundary value problem; canonical matrix

Mathematics Subject Classification


31A25; 35J25

References


Akhalaia, G. and G. Manjavidze. "Boundary value problems of the theory of generalized analytic vectors." Complex methods for partial differential equations. Vol. 6. Dordecht: Kluwer Acad. Publ., 1999. 57-97.

Manjavidze, N. "Boundary value problems for analytic and generalized analytic functions on a cut plane." Mem. Differential Equations Math. Phys. 33 (2004): 121-154.

Manjavidze, G. "Boundary value problems for analytic and generalized functions." Some Topics on Value Distribution and Differentiability in Complex and P-adic Analysis. Vol. 11. Beijing: Science Press, 2008. 499-631.

Manjavidze, G. and N. Manjavidze. "Boundary value problems for generalized analytic functions." J. Math. Sci. vol. 160.6 (2009): 745-821.


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