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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2407.09406 |
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| _version_ | 1866916320773144576 |
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| author | Parrish, Andrew Rosenblatt, Joseph |
| author_facet | Parrish, Andrew Rosenblatt, Joseph |
| contents | We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures $μ_n$ on $\mathbb R$. If this sequence of operators constitutes an approximate identity on a particular class of functions $\mathcal F$, under what additional conditions do we have $μ_n \ast f \to f$ a.e. for all $f \in \mathcal F$? We focus on the particular case of a sequence of contractions $C_{t_n}μ$ of a single probability measure $μ$, with $t_n \to 0$, so that that the sequence of operators is an approximate identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pointwise Convergence of Sequences of Singular Measures Parrish, Andrew Rosenblatt, Joseph Dynamical Systems Classical Analysis and ODEs Probability 42A05, 42A45, 60B10 We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures $μ_n$ on $\mathbb R$. If this sequence of operators constitutes an approximate identity on a particular class of functions $\mathcal F$, under what additional conditions do we have $μ_n \ast f \to f$ a.e. for all $f \in \mathcal F$? We focus on the particular case of a sequence of contractions $C_{t_n}μ$ of a single probability measure $μ$, with $t_n \to 0$, so that that the sequence of operators is an approximate identity. |
| title | Pointwise Convergence of Sequences of Singular Measures |
| topic | Dynamical Systems Classical Analysis and ODEs Probability 42A05, 42A45, 60B10 |
| url | https://arxiv.org/abs/2407.09406 |