The Schur algorithm, reproducing kernel spaces and system theory. Transl. from the French by Stephen S. Wilson (Q2743924)

This edition is the translation into English of French original (1998; Zbl 0946.93002). We have to add to that detailed review our remark that many typos (though not all) and sometimes lack of definitions of some quantities have been corrected in this new edition. Unfortunately, the ambiguity of notations in some places of the book still remains (thus, \(\alpha\) in Theorem~4.4.3, page 72, in the expression for \(\phi\) is not the same as the one in \(R_\alpha\) a few lines later, \(X\) is an operator and a discriminant curve, page 130 and 131). We like to agree with the conclusion of the review mentioned above: ``This excellent survey showing a rich interplay between functional analysis, complex analysis, and systems science is very informative and can be highly recommended to functional analysts curious about the systems science impact of their discipline or to theoretically inclined systems scientists, in particular those involved in the realization theory.''