A pluripotential theoretic framework for polynomial interpolation of vector-valued functions and differential forms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916681164521472 |
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| author | Bruno, Ludovico Bruni Piazzon, Federico |
| author_facet | Bruno, Ludovico Bruni Piazzon, Federico |
| contents | We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the proposed modification a vector valued weight is considered, allowing to partially extend the main asymptotic results holding for interpolation of scalar valued functions to the case of vector valued ones. As motivating example and main application we specialize our results to interpolation of differential forms by differential forms with polynomial coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A pluripotential theoretic framework for polynomial interpolation of vector-valued functions and differential forms Bruno, Ludovico Bruni Piazzon, Federico Complex Variables We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the proposed modification a vector valued weight is considered, allowing to partially extend the main asymptotic results holding for interpolation of scalar valued functions to the case of vector valued ones. As motivating example and main application we specialize our results to interpolation of differential forms by differential forms with polynomial coefficients. |
| title | A pluripotential theoretic framework for polynomial interpolation of vector-valued functions and differential forms |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2504.06745 |