Spectral convergence of empirical integral operators with discontinuous kernels
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913021651058688 |
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| author | Dias, Manuel |
| author_facet | Dias, Manuel |
| contents | We study the spectral behavior as the sample size $n \to +\infty$ of integral operators defined by convolution of a non-negative symmetric kernel k with respect to empirical measures $μ_n = \frac{1}{n} \sum_{i=1}^n δ_{X_i}$, where $\{X_i\}_{i=1}^n$ are independent uniform samples from a compact probability metric space $(\mathcal{X},d,μ)$. Relaxing the usual positivity and continuity assumptions on k, we prove the convergence of these empirical operators to their continuous counterparts, and provide explicit convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09355 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral convergence of empirical integral operators with discontinuous kernels Dias, Manuel Spectral Theory Functional Analysis Probability 60B20, 47A10, 45P05 We study the spectral behavior as the sample size $n \to +\infty$ of integral operators defined by convolution of a non-negative symmetric kernel k with respect to empirical measures $μ_n = \frac{1}{n} \sum_{i=1}^n δ_{X_i}$, where $\{X_i\}_{i=1}^n$ are independent uniform samples from a compact probability metric space $(\mathcal{X},d,μ)$. Relaxing the usual positivity and continuity assumptions on k, we prove the convergence of these empirical operators to their continuous counterparts, and provide explicit convergence rates. |
| title | Spectral convergence of empirical integral operators with discontinuous kernels |
| topic | Spectral Theory Functional Analysis Probability 60B20, 47A10, 45P05 |
| url | https://arxiv.org/abs/2604.09355 |