On a new notion of holomorphy and its applications

Wolfgang Sproessig; Le Thu Hoai

Authors

Wolfgang Sproessig Freiberg University of Mining and Technology, Faculty of Mathematics and Informatics, Agricola-Strasse 1, 09596 Freiberg, Germany.
Le Thu Hoai Hanoi University of Technology, Faculty for Applied Mathematics and Informatics, Dai Co Viet Street 1, 10000 Hanoi, Vietnam.

Keywords:

Generalized holomorphic functions, Taylor-Gontcharov formulae, Plemelj projections, higher order boundary value problems

Abstract

This paper devotes a new general notion of holomorphy which works in the continous and discrete cases. With the help of methods of a general operator theory the so called L-holomorphy is introduced. Realizations of this calculus follow. New versions of Taylor- and Taylor–Gontcharov formulae are deduced. The results are applied for the solution of higher order systems of differential equations.