Spectral algorithms in higher-order Fourier analysis
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913659302707200 |
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| author | Candela, Pablo González-Sánchez, Diego Szegedy, Balázs |
| author_facet | Candela, Pablo González-Sánchez, Diego Szegedy, Balázs |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral algorithms in higher-order Fourier analysis Candela, Pablo González-Sánchez, Diego Szegedy, Balázs Combinatorics Spectral Theory 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. |
| title | Spectral algorithms in higher-order Fourier analysis |
| topic | Combinatorics Spectral Theory |
| url | https://arxiv.org/abs/2501.12287 |