On the Theory of Matrix Valued Functions Belonging to the Smirnov Class
| dc.creator | Katsnelson, Victor | |
| dc.creator | Kirstein, Bernd | |
| dc.date | 2007-06-13 | |
| dc.date.accessioned | 2026-07-07T08:09:50Z | |
| dc.date.available | 2026-07-07T08:09:50Z | |
| dc.description | A theory of matrix-valued functions from the matricial Smirnov class ${\goth N}_n^+({\Bbb D})$ is systematically developed. In particular, the maximum principle of V.I.Smirnov, inner-outer factorization, the Smirnov-Beurling characterization of outer functions and an analogue of Frostman's theorem are presented for matrix-valued functions from the Smirnov class ${\goth N}_n^+({\Bbb D})$. We also consider a family $F_λ =F-λI$ of functions belonging to the matricial Smirnov class which is indexed by a complex parameter $λ$. We show that with the exception of a ''very small'' set of such $λ$ the corresponding inner factor in the inner-outer factorization of the function $F_λ$ is a Blaschke-Potapov product. The main goal of this paper is to provide users of analytic matrix-function theory with a standard source for references related to the matricial Smirnov class. | |
| dc.identifier | https://arxiv.org/abs/0706.1901 | |
| dc.identifier | http://arxiv.org/abs/0706.1901 | |
| dc.identifier | Topics in Interpolation Theory. Operator Theory: Advances and Applications, Vol. 95. Birkhauser 1997 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131659 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 30D50, 46E10 | |
| dc.title | On the Theory of Matrix Valued Functions Belonging to the Smirnov Class | |
| dc.type | text |