Greedy Expansions with Prescribed Coefficients in Hilbert Spaces
Greedy expansions with prescribed coefficients, which have been studied by V. N. Temlyakov in Banach spaces, are considered here in a narrower case of Hilbert spaces. We show that in this case the positive result on the convergence does not require monotonicity of coefficient sequence C. Furthermore...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/4867091 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849473052886171648 |
|---|---|
| author | Artur R. Valiullin Albert R. Valiullin Vladimir V. Galatenko |
| author_facet | Artur R. Valiullin Albert R. Valiullin Vladimir V. Galatenko |
| author_sort | Artur R. Valiullin |
| collection | DOAJ |
| description | Greedy expansions with prescribed coefficients, which have been studied by V. N. Temlyakov in Banach spaces, are considered here in a narrower case of Hilbert spaces. We show that in this case the positive result on the convergence does not require monotonicity of coefficient sequence C. Furthermore, we show that the condition sufficient for the convergence, namely, the inclusion C∈l2∖l1, can not be relaxed at least in the power scale. At the same time, in finite-dimensional spaces, the condition C∈l2 can be replaced by convergence of C to zero. |
| format | Article |
| id | doaj-art-db7ff0e9ec424926a702df7cae26b84b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-db7ff0e9ec424926a702df7cae26b84b2025-08-20T03:24:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/48670914867091Greedy Expansions with Prescribed Coefficients in Hilbert SpacesArtur R. Valiullin0Albert R. Valiullin1Vladimir V. Galatenko2Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, RussiaFaculty of Mechanics and Mathematics, Lomonosov Moscow State University, RussiaFaculty of Mechanics and Mathematics, Lomonosov Moscow State University, RussiaGreedy expansions with prescribed coefficients, which have been studied by V. N. Temlyakov in Banach spaces, are considered here in a narrower case of Hilbert spaces. We show that in this case the positive result on the convergence does not require monotonicity of coefficient sequence C. Furthermore, we show that the condition sufficient for the convergence, namely, the inclusion C∈l2∖l1, can not be relaxed at least in the power scale. At the same time, in finite-dimensional spaces, the condition C∈l2 can be replaced by convergence of C to zero.http://dx.doi.org/10.1155/2018/4867091 |
| spellingShingle | Artur R. Valiullin Albert R. Valiullin Vladimir V. Galatenko Greedy Expansions with Prescribed Coefficients in Hilbert Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Greedy Expansions with Prescribed Coefficients in Hilbert Spaces |
| title_full | Greedy Expansions with Prescribed Coefficients in Hilbert Spaces |
| title_fullStr | Greedy Expansions with Prescribed Coefficients in Hilbert Spaces |
| title_full_unstemmed | Greedy Expansions with Prescribed Coefficients in Hilbert Spaces |
| title_short | Greedy Expansions with Prescribed Coefficients in Hilbert Spaces |
| title_sort | greedy expansions with prescribed coefficients in hilbert spaces |
| url | http://dx.doi.org/10.1155/2018/4867091 |
| work_keys_str_mv | AT arturrvaliullin greedyexpansionswithprescribedcoefficientsinhilbertspaces AT albertrvaliullin greedyexpansionswithprescribedcoefficientsinhilbertspaces AT vladimirvgalatenko greedyexpansionswithprescribedcoefficientsinhilbertspaces |