| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | Results in Mathematics; v. 74, n. 2 JUN 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
Approximation processes in the reproducing kernel Hilbert space associated to a continuous kernel on the unit sphere Sm in the Euclidean space Rm+1 are known to depend upon the Mercer's expansion of the compact and self-adjoint L2(Sm)-operator associated to the kernel. The estimation of the Kolmogorov nth width of the unit ball of the reproducing kernel Hilbert space in L2(Sm) and the identification of the so-called optimal subspace usually suffice. These Kolmogorov widths can be computed through the eigenvalues of the integral operator associated to the kernel. This paper provides sharp upper bounds for the Kolmogorov widths in the case in which the kernel satisfies an abstract Holder condition. In particular, we follow the opposite direction usually considered in the literature, that is, we estimate the widths from decay rates for the sequence of eigenvalues of the integral operator. (AU) | |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 16/02847-9 - Characterizations of fractional order K-functionals and its applications |
| Grantee: | Thaís Jordão |
| Support Opportunities: | Regular Research Grants |