Improper Poisson integral of the sinc function
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917980546269184 |
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| author | Szulga, Jerzy |
| author_facet | Szulga, Jerzy |
| contents | A formal sum $\sum_n f(S_n)$ may be seen as the integral $\int f dN$ with respect to random point process $N(A)=|\{n:S_n\in A\}|$. We study its convergence beyond the well known context of Lebesgue integrable functions, admitting nonintegrable functions whose improper Riemann-Lebesgue integrals exist. We focus on the sinc function and some of its relations leaving the general case to conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improper Poisson integral of the sinc function Szulga, Jerzy Probability Primary 60H05. Secondary 60F25 A formal sum $\sum_n f(S_n)$ may be seen as the integral $\int f dN$ with respect to random point process $N(A)=|\{n:S_n\in A\}|$. We study its convergence beyond the well known context of Lebesgue integrable functions, admitting nonintegrable functions whose improper Riemann-Lebesgue integrals exist. We focus on the sinc function and some of its relations leaving the general case to conjectures. |
| title | Improper Poisson integral of the sinc function |
| topic | Probability Primary 60H05. Secondary 60F25 |
| url | https://arxiv.org/abs/2504.05574 |