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Functional models, unitary invariants, mosaics and principal functions for operators with trace class self-commutator
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 1, pp. 18-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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The singular integral model of an operator with trace class self-commutator is constructed. A decomposition theorem for operators in orthogonal sum of normal and completely nonnormal operators is obtained. A notion of the hyponormal metrical colligation is introduced, and it is proved that the determining and characteristic functions are unitary invariants for the simple colligations. A class of functions, which are the semidetermining functions is described. On the base of the singular integral model the mosaics and the Pincus principal functions are constructed. 
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     author = {I. V. Vorobyov},
     title = {Functional models, unitary invariants, mosaics and principal functions for operators with trace class self-commutator},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {18--47},
     year = {2002},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2002_9_1_a1/}
}
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I. V. Vorobyov. Functional models, unitary invariants, mosaics and principal functions for operators with trace class self-commutator. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 1, pp. 18-47. http://geodesic.mathdoc.fr/item/JMAG_2002_9_1_a1/