Ilya Vyugin

On the Riemann-Hilbert Problem for Difference and q-Difference Equations

We study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems.
A generalization of Birkhoff's existence theorem is presented. We prove that for any admissible set of characteristic constants there exists a system
$$
Y(z+1)=A(z)Y(z) \text{ or } Y(qz)=Q(z)Y(z),
$$
which has the given constants.

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University of Bialystok