Advancements in nonlinear exponential sampling: convergence, quantitative analysis and Voronovskaya-type formula
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912528924147712 |
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| author | Costarelli, Danilo Natale, Mariarosaria |
| author_facet | Costarelli, Danilo Natale, Mariarosaria |
| contents | In this paper, we introduce the nonlinear exponential Kantorovich sampling series. We establish pointwise and uniform convergence properties and a nonlinear asymptotic formula of the Voronovskaja-type given in terms of the limsup. Furthermore, we extend these convergence results to Mellin-Orlicz spaces with respect to the logarithmic (Haar) measure. Quantitative results are also given, using the log-modulus of continuity and the log-modulus of smoothness, respectively, for log-uniformly continuous functions and for functions in Mellin-Orlicz spaces. Consequently, the qualitative order of convergence can be obtained in case of functions belonging to suitable Lipschitz (log-Hölderian) classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Advancements in nonlinear exponential sampling: convergence, quantitative analysis and Voronovskaya-type formula Costarelli, Danilo Natale, Mariarosaria Functional Analysis In this paper, we introduce the nonlinear exponential Kantorovich sampling series. We establish pointwise and uniform convergence properties and a nonlinear asymptotic formula of the Voronovskaja-type given in terms of the limsup. Furthermore, we extend these convergence results to Mellin-Orlicz spaces with respect to the logarithmic (Haar) measure. Quantitative results are also given, using the log-modulus of continuity and the log-modulus of smoothness, respectively, for log-uniformly continuous functions and for functions in Mellin-Orlicz spaces. Consequently, the qualitative order of convergence can be obtained in case of functions belonging to suitable Lipschitz (log-Hölderian) classes. |
| title | Advancements in nonlinear exponential sampling: convergence, quantitative analysis and Voronovskaya-type formula |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2411.15475 |