# Nearly tight frames of spin wavelets on the sphere

## TL;DR

This paper demonstrates that spin wavelets on the sphere can be constructed as nearly tight frames, facilitating analysis of cosmic microwave background polarization with localized frame elements.

## Contribution

It introduces a method to form nearly tight frames of spin wavelets on the sphere, improving their applicability in astrophysical data analysis.

## Key findings

- Spin wavelets can form nearly tight frames on the sphere.
- Frame elements are localized within geodesic balls.
- Application to polarization analysis of cosmic microwave background.

## Abstract

We show that the spin wavelets on the sphere $S^2$, which were constructed by the first author and Marinucci in an earlier article, can be chosen so as to form a nearly tight frame. These spin wavelets can be applied to the study of the polarization of cosmic microwave background radiation. For certain of these frames, there is a positive $C$ such that each frame element at scale $a^j$ is supported in a geodesic ball of radius $Ca^j$.