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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.09775 |
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| _version_ | 1866910657582989312 |
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| author | Lopushansky, Oleh |
| author_facet | Lopushansky, Oleh |
| contents | We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in Lebesgue's spaces by decreasing rearrangements $f^*$ with the help of approximation $E$-functionals, error estimates are found. Examples of numerical calculations and spectral approximations of self-adjoint operators obtained by obtained estimates are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some exact constants for bilateral approximations in quasi-normed groups Lopushansky, Oleh Functional Analysis 42B35, 41A44, 41A17, 46B70 We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in Lebesgue's spaces by decreasing rearrangements $f^*$ with the help of approximation $E$-functionals, error estimates are found. Examples of numerical calculations and spectral approximations of self-adjoint operators obtained by obtained estimates are given. |
| title | Some exact constants for bilateral approximations in quasi-normed groups |
| topic | Functional Analysis 42B35, 41A44, 41A17, 46B70 |
| url | https://arxiv.org/abs/2405.09775 |