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| In mathematics, the '''Schur class''' consists of the '''Schur functions''': the holomorphic functions from the open unit disk to the closed unit disk. These functions were studied by {{harvs|txt|last=Schur|year=1918|authorlink=Issai Schur}}.
| | 59 year old Book or Script Editor Stephan from Sault-au-Mouton, usually spends time with pastimes like creating, property developers [http://hhwok.com/?option=com_k2&view=itemlist&task=user&id=16708 housing in singapore] singapore and greeting card collecting. Enjoys travel and was stimulated after making a vacation to Ancient City of Ping Yao. |
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| The '''Schur parameters''' γ<sub>''j''</sub> of a Schur function ''f''<sub>0</sub> are defined recursively by
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| :<math> \gamma_j=f_j(0)</math>
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| :<math>zf_{j+1}=\frac{f_j(z)-\gamma_j}{1-\overline{\gamma_j}f_j(z)}.</math>
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| The Schur parameters γ<sub>''j''</sub> all have absolute value at most 1.
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| This gives a [[continued fraction]] expansion of the Schur function ''f''<sub>0</sub> by repeatedly using the fact that
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| :<math> f_j(z)=\gamma_j+\frac{1-|\gamma_j|^2}{\overline {\gamma_j}+\frac{1}{zf_{j+1}(z)}}</math>
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| which gives
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| :<math> f_0(z)=\gamma_0+\frac{1-|\gamma_0|^2}{\overline {\gamma_0}+\frac{1}{z \gamma_1+\frac{z(1-|\gamma_1|^2)}{\overline {\gamma_1}+\frac{1}{z\gamma_2+\cdots}}}}.</math>
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| ==References==
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| *{{citation|last=Schur|first=I. |title=Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. I, II
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| |journal = J. Reine Angew. Math.
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| |volume = 147,
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| |pages = 205–232
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| |year = 1918
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| |publisher = Walter de Gruyter|place= Berlin
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| |language = German
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| |DOI = 10.1515/crll.1917.147.205
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| |zbl = 46.0475.01
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| }}
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| *{{Citation | last1=Simon | first1=Barry | author1-link=Barry Simon | title=Orthogonal polynomials on the unit circle. Part 1. Classical theory | url=http://books.google.com/books?id=d94r7kOSnKcC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=American Mathematical Society Colloquium Publications | isbn=978-0-8218-3446-6 | mr=2105088 | year=2005 | volume=54}}
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| *{{Citation | last1=Simon | first1=Barry | author1-link=Barry Simon | title=Orthogonal polynomials on the unit circle. Part 2. Spectral theory | url=http://books.google.com/books?id=54juCPc3ulwC | publisher=[[American Mathematical Society]] | location=Providence, R.I. | series=American Mathematical Society Colloquium Publications | isbn=978-0-8218-3675-0 | mr=2105089 | year=2005 | volume=54}}
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| [[Category:Complex analysis]]
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59 year old Book or Script Editor Stephan from Sault-au-Mouton, usually spends time with pastimes like creating, property developers housing in singapore singapore and greeting card collecting. Enjoys travel and was stimulated after making a vacation to Ancient City of Ping Yao.