Greedy Expansions with Prescribed Coefficients in Hilbert Spaces
| Autor: | Vladimir V. Galatenko, Albert R. Valiullin, Artur R. Valiullin |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Sequence
Pure mathematics Article Subject lcsh:Mathematics 010102 general mathematics Hilbert space Banach space Zero (complex analysis) Scale (descriptive set theory) Monotonic function 010103 numerical & computational mathematics lcsh:QA1-939 01 natural sciences Power (physics) symbols.namesake Mathematics (miscellaneous) Convergence (routing) symbols 0101 mathematics Mathematics |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2018 (2018) |
| ISSN: | 0161-1712 |
| DOI: | 10.1155/2018/4867091 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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