# Discrete Spectra of Convolutions on Disks using Sturm-Liouville Theory

## TL;DR

This paper explores the spectral properties of convolutions on disks using Sturm-Liouville theory, analyzing boundary conditions and their effects on the spectra of functions supported on circular domains.

## Contribution

It introduces a systematic approach to analyze discrete spectra of convolutions on disks through Sturm-Liouville theory, including boundary condition considerations.

## Key findings

- Spectral analysis of convolutions on disks using Sturm-Liouville theory
- Impact of boundary conditions on spectral properties
- Development of analytic methods for discrete spectra

## Abstract

This paper presents a systematic study for analytic aspects of discrete spectra methods for convolution of functions supported on disks, according to the Sturm-Liouville theory. We then investigate different aspects of the presented theory in the cases of zero-value boundary condition and derivative boundary condition.