# A local Levinson theorem for compact symmetric spaces

## TL;DR

This paper extends Levinson's classical theorem, which links the vanishing of functions on a subset to Fourier coefficient decay, to the setting of compact symmetric spaces.

## Contribution

It establishes an analogue of Levinson's theorem for functions on compact symmetric spaces, broadening the theorem's applicability.

## Key findings

- Proves a Levinson-type theorem on compact symmetric spaces.
- Connects function vanishing properties with Fourier coefficient decay in this setting.
- Provides a new theoretical framework for harmonic analysis on symmetric spaces.

## Abstract

A classical result due to Levinson characterizes the existence of non-zero functions defined on a circle vanishing on an open subset of the circle in terms of the pointwise decay of their Fourier coefficients [13]. We prove certain analogue of this result on compact symmetric spaces.