# Density results for continuous frames

## TL;DR

This paper establishes necessary density conditions for the localization of continuous frames and applies these results to sampling and interpolation in broad classes of reproducing kernel Hilbert spaces.

## Contribution

It introduces new density criteria for continuous frames and extends these to sampling and interpolation in various reproducing kernel Hilbert spaces.

## Key findings

- Necessary conditions for frame localization based on Beurling densities
- Density conditions for sampling in reproducing kernel Hilbert spaces
- Density criteria for interpolation in these spaces

## Abstract

We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of reproducing kernel Hilbert spaces.