# Interpolating and sampling sequences in finite Riemann surfaces

## TL;DR

This paper characterizes the conditions for sequences to be interpolating or sampling in a space of holomorphic functions with growth restrictions on finite Riemann surfaces.

## Contribution

It offers a new description of interpolating and sampling sequences specifically for holomorphic functions on finite Riemann surfaces with growth constraints.

## Key findings

- Characterization of interpolating sequences
- Characterization of sampling sequences
- Applicable to holomorphic functions with growth restrictions

## Abstract

We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.