On optimization of cubature formulae for Sobolev classes of functions defined on star domains
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914734994882560 |
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| author | Kovalenko, Oleg |
| author_facet | Kovalenko, Oleg |
| contents | We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm of their distributional gradient; thus we generalize the known solution of this optimization problem in the case, when the domain of definition of the functions is convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03154 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On optimization of cubature formulae for Sobolev classes of functions defined on star domains Kovalenko, Oleg Functional Analysis 41A55, 41A44, 26D10 We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm of their distributional gradient; thus we generalize the known solution of this optimization problem in the case, when the domain of definition of the functions is convex. |
| title | On optimization of cubature formulae for Sobolev classes of functions defined on star domains |
| topic | Functional Analysis 41A55, 41A44, 26D10 |
| url | https://arxiv.org/abs/2308.03154 |