Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910460268249088 |
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| author | Angeloni, Laura Costarelli, Danilo Darielli, Chiara |
| author_facet | Angeloni, Laura Costarelli, Danilo Darielli, Chiara |
| contents | In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its square. In particular, we prove uniform convergence, by means of two different approaches, as well as a quantitative estimate of the order of approximation in terms of the modulus of continuity of the approximated function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16935 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube Angeloni, Laura Costarelli, Danilo Darielli, Chiara Classical Analysis and ODEs Functional Analysis In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its square. In particular, we prove uniform convergence, by means of two different approaches, as well as a quantitative estimate of the order of approximation in terms of the modulus of continuity of the approximated function. |
| title | Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2405.16935 |