Multilinear approximate identities generated by hypermetrics on spaces of homogeneous type
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917236730494976 |
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| author | Aimar, Hugo Gómez, Ivana Toledo, Joaquín |
| author_facet | Aimar, Hugo Gómez, Ivana Toledo, Joaquín |
| contents | The classical Newtonian potentials, defined in terms of metrics, give rise to the basic family of kernels defining linear integral operators and posing the fundamental problems of linear harmonic analysis. When the binary character of a metric on a set is naturally generalized to the $(k+1)$-ary character of hypermetric on the set, we obtain families of kernels of $k+1$ variables leading to multilinear integral operators of order $k$ or $k$-linear operators. In this paper we consider the problem of multilinear approximation to the multilinear identity through potentials built on hypermetrics in the general setting of spaces of homogeneous type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00326 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multilinear approximate identities generated by hypermetrics on spaces of homogeneous type Aimar, Hugo Gómez, Ivana Toledo, Joaquín Classical Analysis and ODEs 42B25 The classical Newtonian potentials, defined in terms of metrics, give rise to the basic family of kernels defining linear integral operators and posing the fundamental problems of linear harmonic analysis. When the binary character of a metric on a set is naturally generalized to the $(k+1)$-ary character of hypermetric on the set, we obtain families of kernels of $k+1$ variables leading to multilinear integral operators of order $k$ or $k$-linear operators. In this paper we consider the problem of multilinear approximation to the multilinear identity through potentials built on hypermetrics in the general setting of spaces of homogeneous type. |
| title | Multilinear approximate identities generated by hypermetrics on spaces of homogeneous type |
| topic | Classical Analysis and ODEs 42B25 |
| url | https://arxiv.org/abs/2602.00326 |