期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2018
卷号：2018
DOI：10.1155/2018/4867091
出版社：Hindawi Publishing Corporation
摘要：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.
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