Analytic holonomicity of real C$^{\mathrm{exp}}$-class distributions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915738468483072 |
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| author | Aizenbud, Avraham Cluckers, Raf Raibaut, Michel Servi, Tamara |
| author_facet | Aizenbud, Avraham Cluckers, Raf Raibaut, Michel Servi, Tamara |
| contents | We introduce a notion of distributions on $\mathbb{R}^n$, called distributions of C$^{\mathrm{exp}}$-class, based on wavelet transforms of distributions and the theory from Cluckers, Comte, Miller, Rolin, Servi (2018) about C$^{\mathrm{exp}}$-class functions. We prove that the framework of C$^{\mathrm{exp}}$-class distributions is closed under natural operations, like push-forward, pull-back, derivation and anti-derivation, and, in the tempered case, Fourier transforms. Our main result is the (real analytic) holonomicity of all distributions of C$^{\mathrm{exp}}$-class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic holonomicity of real C$^{\mathrm{exp}}$-class distributions Aizenbud, Avraham Cluckers, Raf Raibaut, Michel Servi, Tamara Algebraic Geometry Logic Representation Theory We introduce a notion of distributions on $\mathbb{R}^n$, called distributions of C$^{\mathrm{exp}}$-class, based on wavelet transforms of distributions and the theory from Cluckers, Comte, Miller, Rolin, Servi (2018) about C$^{\mathrm{exp}}$-class functions. We prove that the framework of C$^{\mathrm{exp}}$-class distributions is closed under natural operations, like push-forward, pull-back, derivation and anti-derivation, and, in the tempered case, Fourier transforms. Our main result is the (real analytic) holonomicity of all distributions of C$^{\mathrm{exp}}$-class. |
| title | Analytic holonomicity of real C$^{\mathrm{exp}}$-class distributions |
| topic | Algebraic Geometry Logic Representation Theory |
| url | https://arxiv.org/abs/2403.20167 |