The Schur algorithm and coefficient characterizations for generalized Schur functions. (English) Zbl 0951.30016
Two problems of generalized Schur functions were dealt with: the Schur algorithm for generalized Schur classes and the Carathéodory coefficient estimation. Both questions were also studied by G. Christner and J. Rovnyak [Contemp. Math. 189, 135-160 (1995; Zbl 0837.47011)]. The existence of the Schur algorithm for generalized Schur classes was analyzed. A condition was found that makes the Schur algorithm work in the generalized Schur classes \(S({\mathcal U},{\mathcal Y})\) \(({\mathcal U},{\mathcal Y}\) are Kreĭn spaces). A characterization of the functions in a Schur class in terms of the Taylor coefficients was obtained. The Carathéodory type interpolation problems were discussed. Two versions of the generalized Carathéodory problem are presented.
Reviewer: V.Burjan (Praha)
MSC:
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 47B50 | Linear operators on spaces with an indefinite metric |
| 30E05 | Moment problems and interpolation problems in the complex plane |
Keywords:
coefficient characterization; interpolation problems; Schur functions; Kreĭn spaces; Carathéodory problemCitations:
Zbl 0837.47011References:
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