On normal Hankel matrices

The problem of characterizing normal Hankel matrices is still far from being solved completely. Partial results available mainly are 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 $\phi$-circulants.