Positive semidefinite analytic functions on real analytic surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910306083536896 |
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| author | Fernando, José F. |
| author_facet | Fernando, José F. |
| contents | Let $X\subset{\mathbb R}^n$ be a (global) real analytic surface. Then every positive semidefinite meromorphic function on $X$ is a sum of $10$ squares of meromorphic functions on $X$. As a consequence, we provide a real Nullstellensatz for (global) real analytic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive semidefinite analytic functions on real analytic surfaces Fernando, José F. Complex Variables Algebraic Geometry Primary: 14P99, 11E25, 32S05, Secondary: 32B10 Let $X\subset{\mathbb R}^n$ be a (global) real analytic surface. Then every positive semidefinite meromorphic function on $X$ is a sum of $10$ squares of meromorphic functions on $X$. As a consequence, we provide a real Nullstellensatz for (global) real analytic surfaces. |
| title | Positive semidefinite analytic functions on real analytic surfaces |
| topic | Complex Variables Algebraic Geometry Primary: 14P99, 11E25, 32S05, Secondary: 32B10 |
| url | https://arxiv.org/abs/2401.12565 |