The Factorization Method in the Abstract Riemann Problem

Abstract

The previously considered schemes for solving the abstract Riemann problem generalize not only the Riemann boundary value problems in Holder space and Lp, but and some integral convolution type equations (with two kernels, Wiener–Hopf, pair ones) in the space L2 ( ) and in wider spaces generalized functions. The corresponding Riemann problem is no longer a boundary problem for analytic functions. However, despite on the whole generality, the matrix Riemann boundary-value problem on a closed contour does not obey to the considered schemes. In this paper, for solving the Riemann problem, an abstact scheme with another axiomatic is proposed, which eliminates this disadvantage.