Bibliographic Details
| Title: |
Spectral algorithms in higher-order Fourier analysis |
| Authors: |
Candela, Pablo, González-Sánchez, Diego, Szegedy, Balázs |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Combinatorics, Mathematics - Spectral Theory |
| More Details: |
Our goal is to provide simple and practical algorithms in higher-order Fourier analysis which are based on spectral decompositions of operators. We propose a general framework for such algorithms and provide a detailed analysis of the quadratic case. Our results reveal new spectral aspects of the theory underlying higher-order Fourier analysis. Along these lines, we prove new inverse and regularity theorems for the Gowers norms based on higher-order character decompositions. Using these results, we prove a spectral inverse theorem and a spectral regularity theorem in quadratic Fourier analysis.
Comment: 71 pages |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2501.12287 |
| Accession Number: |
edsarx.2501.12287 |
| Database: |
arXiv |
