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On normal Hankel matrices

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Abstract

The problem of characterizing normal Hankel matrices is still far from being solved completely. The partial results available are mainly the descriptions of certain subsets of the class of normal Hankel matrices. These subsets were found separately and using different arguments. This paper presents a general approach allowing, in particular, to obtain all the known subsets as special cases. Normal Hankel matrices outside of these subsets correspond to the main (and the most difficult) case of our treatment. At the moment, this case defies complete analysis. However, we show that unknown types of normal Hankel matrices can only be found within a new and very interesting matrix class that extends (and contains) the class of φ-circulants. Bibliography: 11 titles.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    Kh. D. Ikramov

  2. Institute of Numerical Mathematics, Moscow, Russia

    V. N. Chugunov

Authors
  1. Kh. D. Ikramov
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  2. V. N. Chugunov
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Correspondence to Kh. D. Ikramov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 63–80.

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Ikramov, K.D., Chugunov, V.N. On normal Hankel matrices. J Math Sci 150, 1951–1960 (2008). https://doi.org/10.1007/s10958-008-0110-4

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  • DOI: https://doi.org/10.1007/s10958-008-0110-4

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