# Frame measures for infinitely many measures

## TL;DR

This paper investigates the existence of frame measures for various spectral measures, demonstrating that infinitely many measures admit both discrete and continuous frame measures, expanding understanding of frame measure existence.

## Contribution

It constructs infinitely many measures that admit both discrete and continuous frame measures, providing new insights into the structure of frame spectral measures.

## Key findings

- Existence of infinitely many measures with frame measures
- Some measures admit both discrete and continuous frame measures
- No general statement for non-frame spectral measures

## Abstract

For every frame spectral measure $ \mu $, there exists a discrete measure $ \nu $ as a frame measure. Since if $ \mu $ is not a frame spectral measure, then there is not any general statement about the existence of frame measures $ \nu $ for $ \mu $, we were motivated to examine Bessel and frame measures. We construct infinitely many measures $ \mu $ which admit frame measures $ \nu $, and we show that there exist infinitely many frame spectral measures $ \mu $ such that besides having a discrete frame measure, they admit continuous frame measures too.