Greedy Expansions with Prescribed Coefficients in Hilbert Spaces

Artur R. Valiullin, Albert R. Valiullin and Vladimir V. Galatenko

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-6

Abstract:

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 . Furthermore, we show that the condition sufficient for the convergence, namely, the inclusion , can not be relaxed at least in the power scale. At the same time, in finite-dimensional spaces, the condition can be replaced by convergence of to zero.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:4867091

DOI: 10.1155/2018/4867091

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