# On the Riemann-Hilbert Problem for Difference and $q$-Difference Systems

## TL;DR

This paper extends the classical Riemann-Hilbert problem to difference and q-difference systems, providing a generalized existence theorem for these classes of equations.

## Contribution

It generalizes Birkhoff's existence theorem to difference and q-difference systems, advancing the theoretical framework of the Riemann-Hilbert problem.

## Key findings

- Generalization of Birkhoff's theorem for difference systems
- Extension of Riemann-Hilbert problem to q-difference systems
- Theoretical foundation for solving difference and q-difference equations

## Abstract

In this paper we study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems. The Birkhoff's existence theorem was generalized in this paper.