Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592706 | Journal of Functional Analysis | 2008 | 27 Pages |
Abstract
The Wiener–Hopf factorization of 2×2 matrix functions and its close relation to scalar Riemann–Hilbert problems on Riemann surfaces is investigated. A family of function classes denoted C(Q1,Q2) is defined. To each class C(Q1,Q2) a Riemann surface Σ is associated, so that the factorization of the elements of C(Q1,Q2) is reduced to solving a scalar Riemann–Hilbert problem on Σ. For the solution of this problem, a notion of Σ-factorization is introduced and a factorization theorem is presented. An example of the factorization of a function belonging to the group of exponentials of rational functions is studied. This example may be seen as typical of applications of the results of this paper to finite-dimensional integrable systems.
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