A topological splitting of the space of meromorphic germs in several variables and continuous evaluators
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910394175455232 |
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| author | Dahmen, Rafael Paycha, Sylvie Schmeding, Alexander |
| author_facet | Dahmen, Rafael Paycha, Sylvie Schmeding, Alexander |
| contents | We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs. Evaluating the resulting holomorphic projection at zero gives rise to a continuous evaluator (at zero) on the space of meromorphic germs in several variables. Our constructions are carried out in the framework of Silva spaces and use an inner product on the underlying space of variables. They generalise to several variables, the topological direct decomposition of meromorphic germs at zero as sums of holomorphic and polar germs previously derived by the first and third author and provide a topological refinement of a known algebraic decomposition of such spaces previously derived by the second author and collaborators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13993 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A topological splitting of the space of meromorphic germs in several variables and continuous evaluators Dahmen, Rafael Paycha, Sylvie Schmeding, Alexander Complex Variables Mathematical Physics 32A70 (primary), 32A20, 46E50, 81T15 (Secondary) We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs. Evaluating the resulting holomorphic projection at zero gives rise to a continuous evaluator (at zero) on the space of meromorphic germs in several variables. Our constructions are carried out in the framework of Silva spaces and use an inner product on the underlying space of variables. They generalise to several variables, the topological direct decomposition of meromorphic germs at zero as sums of holomorphic and polar germs previously derived by the first and third author and provide a topological refinement of a known algebraic decomposition of such spaces previously derived by the second author and collaborators. |
| title | A topological splitting of the space of meromorphic germs in several variables and continuous evaluators |
| topic | Complex Variables Mathematical Physics 32A70 (primary), 32A20, 46E50, 81T15 (Secondary) |
| url | https://arxiv.org/abs/2206.13993 |