XXXVII Workshop on Geometric Methods in Physics | 1-7.07.2018 |

VII School on Geometry and Physics | 25-29.06.2018 |

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## Ilya Vyugin## On the Riemann-Hilbert Problem for Difference and q-Difference EquationsWe 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 |

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