On sharp heat kernel estimates in the context of Fourier-Dini expansions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929547004346368 |
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| author | Langowski, Bartosz Nowak, Adam |
| author_facet | Langowski, Bartosz Nowak, Adam |
| contents | We prove sharp estimates of the heat kernel associated with Fourier-Dini expansions on $(0,1)$ equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result including sharp bounds for the corresponding Poisson and potential kernels, sharp mapping properties of the maximal heat semigroup and potential operators and boundary convergence of the Fourier-Dini semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sharp heat kernel estimates in the context of Fourier-Dini expansions Langowski, Bartosz Nowak, Adam Classical Analysis and ODEs primary 42C05, secondary 35K08 We prove sharp estimates of the heat kernel associated with Fourier-Dini expansions on $(0,1)$ equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result including sharp bounds for the corresponding Poisson and potential kernels, sharp mapping properties of the maximal heat semigroup and potential operators and boundary convergence of the Fourier-Dini semigroup. |
| title | On sharp heat kernel estimates in the context of Fourier-Dini expansions |
| topic | Classical Analysis and ODEs primary 42C05, secondary 35K08 |
| url | https://arxiv.org/abs/2410.12732 |