Interpolation and inverse problems in spectral Barron spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910069814198272 |
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| author | Lu, Shuai Mathé, Peter |
| author_facet | Lu, Shuai Mathé, Peter |
| contents | Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By establishing a connection between these spaces and a specific positive linear operator, we investigate the interpolation and scaling relationships among diverse spectral Barron spaces. Furthermore, we introduce a link condition by relating the spectral Barron space to inverse problems, illustrating this with three exemplary cases. We revisit the notion of universal approximation within the context of spectral Barron spaces and validate an error bound for Tikhonov regularization, penalized by the spectral Barron norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpolation and inverse problems in spectral Barron spaces Lu, Shuai Mathé, Peter Numerical Analysis Functional Analysis 65J20, 68T07, 41A05 Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By establishing a connection between these spaces and a specific positive linear operator, we investigate the interpolation and scaling relationships among diverse spectral Barron spaces. Furthermore, we introduce a link condition by relating the spectral Barron space to inverse problems, illustrating this with three exemplary cases. We revisit the notion of universal approximation within the context of spectral Barron spaces and validate an error bound for Tikhonov regularization, penalized by the spectral Barron norm. |
| title | Interpolation and inverse problems in spectral Barron spaces |
| topic | Numerical Analysis Functional Analysis 65J20, 68T07, 41A05 |
| url | https://arxiv.org/abs/2502.03819 |