Approximation by linear sampling operators in Banach spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911401698656256 |
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| author | Kolomoitsev, Yurii |
| author_facet | Kolomoitsev, Yurii |
| contents | This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special $K$-functionals and their realizations by sampling operators, as well as strong converse inequalities, which, to the best of our knowledge, have not been previously established for sampling operators even in the classical spaces $L_p$. The results extend several classical theorems previously known mainly in $L_p$ and apply to all functions $f\in X$ for which the corresponding sampling operator is well defined, thereby substantially enlarging the class of functions that can be considered in this framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19012 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximation by linear sampling operators in Banach spaces Kolomoitsev, Yurii Functional Analysis Numerical Analysis Classical Analysis and ODEs 41A05, 41A10, 41A25, 41A27, 42A15, 46B42, 46E30 This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special $K$-functionals and their realizations by sampling operators, as well as strong converse inequalities, which, to the best of our knowledge, have not been previously established for sampling operators even in the classical spaces $L_p$. The results extend several classical theorems previously known mainly in $L_p$ and apply to all functions $f\in X$ for which the corresponding sampling operator is well defined, thereby substantially enlarging the class of functions that can be considered in this framework. |
| title | Approximation by linear sampling operators in Banach spaces |
| topic | Functional Analysis Numerical Analysis Classical Analysis and ODEs 41A05, 41A10, 41A25, 41A27, 42A15, 46B42, 46E30 |
| url | https://arxiv.org/abs/2601.19012 |