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Hankel matrix transforms and operators. (English) Zbl 1309.47028
The article under review concerns Hankel matrices and Hankel operators.
Reviewer’s remark: The paper contains errors. In particular, the paper contains the following result:
Theorem 3.1. A Hankel matrix is regular if and only if
(i) \(\lim_{n\to\infty}h_{n+k}=0\).
(ii) \(\lim_{n\to\infty}\sum_{k=1}^\infty h_{n+k}=1\).
(iii) \(\sup_n\sum_{k=1}^\infty|h_{n+k}|\leq M\).
Condition (i) is very strange. Clearly, \( \lim_{n\to\infty}h_{n+k}=\lim_{n\to\infty}h_n. \)
Condition (iii) does not make any sense. If the series converges, then \(\lim_{n\to\infty}\sum_{k=1}^\infty h_{n+k}=0\).
Condition (iii) is also strange. Clearly, the supremum in question involves a non increasing sequence.

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
41A35 Approximation by operators (in particular, by integral operators)
Full Text: DOI
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