Geodesic
Functional model of bounded operator
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 2, pp. 158-174 Cet article a éte moissonné depuis la source Math-Net.Ru

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The constructing of functional model for any bounded operator $T$ (contracting or not) in Hilbert space $H$ is done. It is shown that existence conditions for wave operarators $W_\pm$ within P. Lax–R. Phillips scattering scheme lead in this case to spaces $l_\beta^2$ with the weight $ \beta.$ These facts lead to Hardy spaces in the ring with the weight $W(e^{i \theta})$ which is defined by the characteristic function $S_\Delta(e^{i\theta})$ of operator $T$. 
@article{JMAG_2001_8_2_a4,
     author = {V. A. Zolotarev},
     title = {Functional model of bounded operator},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {158--174},
     year = {2001},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a4/}
}
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V. A. Zolotarev. Functional model of bounded operator. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 2, pp. 158-174. http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a4/